Sustainability of irrigated farming systems in a Tunisian region: A recursive stochastic programming analysis

The aim of this study was to evaluate the sustainability of farm irrigation systems in the Cébalat district in northern Tunisia. It addressed the challenging topic of sustainable agriculture through a bio-economic approach linking a biophysical model to an economic optimisation model. A crop growth simulation model (CropSyst) was used to build a database to determine the relationships between agricultural practices, crop yields and environmental effects (salt accumulation in soil and leaching of nitrates) in a context of high climatic variability. The database was then fed into a recursive stochastic model set for a 10-year plan that allowed analysing the effects of cropping patterns on farm income, salt accumulation and nitrate leaching. We assumed that the long-term sustainability of soil productivity might be in conflict with farm profitability in the short-term. Assuming a discount rate of 10% (for the base scenario), the model closely reproduced the current system and allowed to predict the degradation of soil quality due to long-term salt accumulation. The results showed that there was more accumulation of salt in the soil for the base scenario than for the alternative scenario (discount rate of 0%). This result was induced by applying a higher quantity of water per hectare for the alternative as compared to a base scenario. The results also showed that nitrogen leaching is very low for the two discount rates and all climate scenarios. In conclusion, the results show that the difference in farm income between the alternative and base scenarios increases over time to attain 45% after 10 years.

Dynamic response of hydro power plants to load variations for providing secondary regulation reserves considering elastic water column effects

In this paper, the dynamic response of a hydro power plant for providing secondary regulation reserve is studied in detail. S pecial emphasis is given to the elastic water column effects both in the penstock and the tailrace tunnel. For this purpose, a nonline ar model based on the analogy between mass and momentum conservation equations of a water conduit and those of wave propagation in transmission lines is used. The influence of the plant configuration and design parameters on the fulfilment of the Spanish Electrical System Operator requirem ents is analysed.

StreamCloud: An elastic and scalable data streaming system

Many applications in several domains such as telecommunications, network security, large scale sensor networks, require online processing of continuous data lows. They produce very high loads that requires aggregating the processing capacity of many nodes. Current Stream Processing Engines do not scale with the input load due to single-node bottlenecks. Additionally, they are based on static con?gurations that lead to either under or over-provisioning. In this paper, we present StreamCloud, a scalable and elastic stream processing engine for processing large data stream volumes. StreamCloud uses a novel parallelization technique that splits queries into subqueries that are allocated to independent sets of nodes in a way that minimizes the distribution overhead. Its elastic protocols exhibit low intrusiveness, enabling effective adjustment of resources to the incoming load. Elasticity is combined with dynamic load balancing to minimize the computational resources used. The paper presents the system design, implementation and a thorough evaluation of the scalability and elasticity of the fully implemented system.

Ab initio Methodology for Calculating Elastic Constant and Sound Velocity for Hydrogen and Deuterium in Molecular Solid Phase

Hydrogen isotopes play a critical role both in inertial and magnetic confinement Nuclear Fusion. Since the preferent fuel needed for this technology is a mixture of deuterium and tritium. The study of these isotopes particularly at very low temperatures carries a technological interest in other applications. The present line promotes a deep study on the structural configuration that hydrogen and deuterium adopt at cryogenic temperatures and at high pressures. Typical conditions occurring in present Inertial Fusion target designs. Our approach is aims to determine the crystal structure characteristics, phase transitions and other parameters strongly correlated to variations of temperature and pressure. With this results is possible calculated the elastic constant and sound velocity for hydrogen and deuterium in molecular solid phase.

Independence, Global analysis, and parallelism, in dinamically scheduled constraint logic programming.

El punto de vista de muchas otras aplicaciones que modifican las reglas de computación. En segundo lugar, y una vez generalizado el concepto de independencia, es necesario realizar un estudio exhaustivo de la efectividad de las herramientas de análisis en la tarea de la paralelizacion automática. Los resultados obtenidos de dicha evaluación permiten asegurar de forma empírica que la utilización de analizadores globales en la tarea de la paralelizacion automática es vital para la consecución de una paralelizarían efectiva. Por último, a la luz de los buenos resultados obtenidos sobre la efectividad de los analizadores de flujo globales basados en la interpretación abstracta, se presenta la generalización de las herramientas de análisis al contexto de los lenguajes lógicos restricciones y planificación dinámica.

Generación de Casos de Prueba en Programación Orientada a Objetos = Test Case Generation in Object-Oriented Programming

Las pruebas de software (Testing) son en la actualidad la técnica más utilizada para la validación y la evaluación de la calidad de un programa. El testing está integrado en todas las metodologías prácticas de desarrollo de software y juega un papel crucial en el éxito de cualquier proyecto de software. Desde las unidades de código más pequeñas a los componentes más complejos, su integración en un sistema de software y su despliegue a producción, todas las piezas de un producto de software deben ser probadas a fondo antes de que el producto de software pueda ser liberado a un entorno de producción. La mayor limitación del testing de software es que continúa siendo un conjunto de tareas manuales, representando una buena parte del coste total de desarrollo. En este escenario, la automatización resulta fundamental para aliviar estos altos costes. La generación automática de casos de pruebas (TCG, del inglés test case generation) es el proceso de generar automáticamente casos de prueba que logren un alto recubrimiento del programa. Entre la gran variedad de enfoques hacia la TCG, esta tesis se centra en un enfoque estructural de caja blanca, y más concretamente en una de las técnicas más utilizadas actualmente, la ejecución simbólica. En ejecución simbólica, el programa bajo pruebas es ejecutado con expresiones simbólicas como argumentos de entrada en lugar de valores concretos. Esta tesis se basa en un marco general para la generación automática de casos de prueba dirigido a programas imperativos orientados a objetos (Java, por ejemplo) y basado en programación lógica con restricciones (CLP, del inglés constraint logic programming). En este marco general, el programa imperativo bajo pruebas es primeramente traducido a un programa CLP equivalente, y luego dicho programa CLP es ejecutado simbólicamente utilizando los mecanismos de evaluación estándar de CLP, extendidos con operaciones especiales para el tratamiento de estructuras de datos dinámicas. Mejorar la escalabilidad y la eficiencia de la ejecución simbólica constituye un reto muy importante. Es bien sabido que la ejecución simbólica resulta impracticable debido al gran número de caminos de ejecución que deben ser explorados y a tamaño de las restricciones que se deben manipular. Además, la generación de casos de prueba mediante ejecución simbólica tiende a producir un número innecesariamente grande de casos de prueba cuando es aplicada a programas de tamaño medio o grande. Las contribuciones de esta tesis pueden ser resumidas como sigue. (1) Se desarrolla un enfoque composicional basado en CLP para la generación de casos de prueba, el cual busca aliviar el problema de la explosión de caminos interprocedimiento analizando de forma separada cada componente (p.ej. método) del programa bajo pruebas, almacenando los resultados y reutilizándolos incrementalmente hasta obtener resultados para el programa completo. También se ha desarrollado un enfoque composicional basado en especialización de programas (evaluación parcial) para la herramienta de ejecución simbólica Symbolic PathFinder (SPF). (2) Se propone una metodología para usar información del consumo de recursos del programa bajo pruebas para guiar la ejecución simbólica hacia aquellas partes del programa que satisfacen una determinada política de recursos, evitando la exploración de aquellas partes del programa que violan dicha política. (3) Se propone una metodología genérica para guiar la ejecución simbólica hacia las partes más interesantes del programa, la cual utiliza abstracciones como generadores de trazas para guiar la ejecución de acuerdo a criterios de selección estructurales. (4) Se propone un nuevo resolutor de restricciones, el cual maneja eficientemente restricciones sobre el uso de la memoria dinámica global (heap) durante ejecución simbólica, el cual mejora considerablemente el rendimiento de la técnica estándar utilizada para este propósito, la \lazy initialization". (5) Todas las técnicas propuestas han sido implementadas en el sistema PET (el enfoque composicional ha sido también implementado en la herramienta SPF). Mediante evaluación experimental se ha confirmado que todas ellas mejoran considerablemente la escalabilidad y eficiencia de la ejecución simbólica y la generación de casos de prueba. ABSTRACT Testing is nowadays the most used technique to validate software and assess its quality. It is integrated into all practical software development methodologies and plays a crucial role towards the success of any software project. From the smallest units of code to the most complex components and their integration into a software system and later deployment; all pieces of a software product must be tested thoroughly before a software product can be released. The main limitation of software testing is that it remains a mostly manual task, representing a large fraction of the total development cost. In this scenario, test automation is paramount to alleviate such high costs. Test case generation (TCG) is the process of automatically generating test inputs that achieve high coverage of the system under test. Among a wide variety of approaches to TCG, this thesis focuses on structural (white-box) TCG, where one of the most successful enabling techniques is symbolic execution. In symbolic execution, the program under test is executed with its input arguments being symbolic expressions rather than concrete values. This thesis relies on a previously developed constraint-based TCG framework for imperative object-oriented programs (e.g., Java), in which the imperative program under test is first translated into an equivalent constraint logic program, and then such translated program is symbolically executed by relying on standard evaluation mechanisms of Constraint Logic Programming (CLP), extended with special treatment for dynamically allocated data structures. Improving the scalability and efficiency of symbolic execution constitutes a major challenge. It is well known that symbolic execution quickly becomes impractical due to the large number of paths that must be explored and the size of the constraints that must be handled. Moreover, symbolic execution-based TCG tends to produce an unnecessarily large number of test cases when applied to medium or large programs. The contributions of this dissertation can be summarized as follows. (1) A compositional approach to CLP-based TCG is developed which overcomes the inter-procedural path explosion by separately analyzing each component (method) in a program under test, stowing the results as method summaries and incrementally reusing them to obtain whole-program results. A similar compositional strategy that relies on program specialization is also developed for the state-of-the-art symbolic execution tool Symbolic PathFinder (SPF). (2) Resource-driven TCG is proposed as a methodology to use resource consumption information to drive symbolic execution towards those parts of the program under test that comply with a user-provided resource policy, avoiding the exploration of those parts of the program that violate such policy. (3) A generic methodology to guide symbolic execution towards the most interesting parts of a program is proposed, which uses abstractions as oracles to steer symbolic execution through those parts of the program under test that interest the programmer/tester most. (4) A new heap-constraint solver is proposed, which efficiently handles heap-related constraints and aliasing of references during symbolic execution and greatly outperforms the state-of-the-art standard technique known as lazy initialization. (5) All techniques above have been implemented in the PET system (and some of them in the SPF tool). Experimental evaluation has confirmed that they considerably help towards a more scalable and efficient symbolic execution and TCG.

Programming assignments automatic grading: review of tools and implementations

Automatic grading of programming assignments is an important topic in academic research. It aims at improving the level of feedback given to students and optimizing the professor time. Several researches have reported the development of software tools to support this process. Then, it is helpfulto get a quickly and good sight about their key features. This paper reviews an ample set of tools forautomatic grading of programming assignments. They are divided in those most important mature tools, which have remarkable features; and those built recently, with new features. The review includes the definition and description of key features e.g. supported languages, used technology, infrastructure, etc. The two kinds of tools allow making a temporal comparative analysis. This analysis infrastructure, etc. The two kinds of tools allow making a temporal comparative analysis. This analysis shows good improvements in this research field, these include security, more language support, plagiarism detection, etc. On the other hand, the lack of a grading model for assignments is identified as an important gap in the reviewed tools. Thus, a characterization of evaluation metrics to grade programming assignments is provided as first step to get a model. Finally new paths in this research field are proposed.

Towards the automatic generation of card games through Grammar-Guided Genetic Programming

We demonstrate generating complete and playable card games using evolutionary algorithms. Card games are represented in a previously devised card game description language, a context-free grammar. The syntax of this language allows us to use grammar-guided genetic programming. Candidate card games are evaluated through a cascading evaluation function, a multi-step process where games with undesired properties are progressively weeded out. Three representa- tive examples of generated games are analysed. We observed that these games are reasonably balanced and have skill ele- ments, they are not yet entertaining for human players. The particular shortcomings of the examples are discussed in re- gard to the generative process to be able to generate quality games

Self-Organizing Architectural design based on Morphogenetic Programming.

In this paper, we present our research into self-organizing building algorithms. This idea of self-organization of animal/plants behaviour interests researchers to explore the mechanisms required for this emergent phenomena and try to apply them in other domains. We were able to implement a typical construction algorithm in a 3D simulation environment and reproduce the results of previous research in the area. LSystems, morphogenetic programming and wasp nest building are explained in order to understand self-organizing models. We proposed Grammatical swarm as a good tool to optimize building structures.

Finite elastic deformations of transversely isotropic circular cylindrical tubes

We consider the finite radially symmetric deformation of a circular cylindrical tube of a homogeneous transversely isotropic elastic material subject to axial stretch, radial deformation and torsion, supported by axial load, internal pressure and end moment. Two different directions of transverse isotropy are considered: the radial direction and an arbitrary direction in planes normal locally to the radial direction, the only directions for which the considered deformation is admissible in general. In the absence of body forces, formulas are obtained for the internal pressure, and the resultant axial load and torsional moment on the ends of the tube in respect of a general strain-energy function. For a specific material model of transversely isotropic elasticity, and material and geometrical parameters, numerical results are used to illustrate the dependence of the pressure, (reduced) axial load and moment on the radial stretch and a measure of the torsional deformation for a fixed value of the axial stretch.

Assessment of the influence of the elastic properties of rail vehicle suspensions on safety, ride quality and track fatigue

A sensitivity analysis has been performed to assess the influence of the elastic properties of railway vehicle suspensions on the vehicle dynamic behaviour. To do this, 144 dynamic simulations were performed modifying, one at a time, the stiffness and damping coefficients, of the primary and secondary suspensions. Three values were assigned to each parameter, corresponding to the percentiles 10, 50 and 90 of a data set stored in a database of railway vehicles.After processing the results of these simulations, the analyzed parameters were sorted by increasing influence. It was also found which of these parameters could be estimated with a lesser degree of accuracy in future simulations without appreciably affecting the simulation results. In general terms, it was concluded that the highest influences were found for the longitudinal stiffness and the lateral stiffness of the primary suspension, and the lowest influences for the vertical stiffness and the vertical damping of the primary suspension, with the parameters of the secondary suspension showing intermediate influences between them.

Inestabilidad de pórticos planos metálicos de edificación con inclusión de la flexibilidad de las uniones y elementos no prismáticos : un enfoque para la optimización

En esta tesis se aborda el problema de la modelización, análisis y optimización de pórticos metálicos planos de edificación frente a los estados límites último y de servicio. El objetivo general es presentar una técnica secuencial ordenada de optimización discreta para obtener el coste mínimo de pórticos metálicos planos de edificación, teniendo en cuenta las especificaciones del EC-3, incorporando las uniones semirrígidas y elementos no prismáticos en el proceso de diseño. Asimismo se persigue valorar su grado de influencia sobre el diseño final. El horizonte es extraer conclusiones prácticas que puedan ser de utilidad y aplicación simple para el proyecto de estructuras metálicas. La cantidad de publicaciones técnicas y científicas sobre la respuesta estructural de entramados metálicos es inmensa; por ello se ha hecho un esfuerzo intenso en recopilar el estado actual del conocimiento, sobre las líneas y necesidades actuales de investigación. Se ha recabado información sobre los métodos modernos de cálculo y diseño, sobre los factores que influyen sobre la respuesta estructural, sobre técnicas de modelización y de optimización, al amparo de las indicaciones que algunas normativas actuales ofrecen sobre el tema. En esta tesis se ha desarrollado un procedimiento de modelización apoyado en el método de los elementos finitos implementado en el entorno MatLab; se han incluido aspectos claves tales como el comportamiento de segundo orden, la comprobación ante inestabilidad y la búsqueda del óptimo del coste de la estructura frente a estados límites, teniendo en cuenta las especificaciones del EC-3. También se ha modelizado la flexibilidad de las uniones y se ha analizado su influencia en la respuesta de la estructura y en el peso y coste final de la misma. Se han ejecutado algunos ejemplos de aplicación y se ha contrastado la validez del modelo con resultados de algunas estructuras ya analizadas en referencias técnicas conocidas. Se han extraído conclusiones sobre el proceso de modelización y de análisis, sobre la repercusión de la flexibilidad de las uniones en la respuesta de la estructura. El propósito es extraer conclusiones útiles para la etapa de proyecto. Una de las principales aportaciones del trabajo en su enfoque de optimización es la incorporación de una formulación de elementos no prismáticos con uniones semirrígidas en sus extremos. Se ha deducido una matriz de rigidez elástica para dichos elementos. Se ha comprobado su validez para abordar el análisis no lineal; para ello se han comparado los resultados con otros obtenidos tras aplicar otra matriz deducida analíticamente existente en la literatura y también mediante el software comercial SAP2000. Otra de las aportaciones de esta tesis es el desarrollo de un método de optimización del coste de pórticos metálicos planos de edificación en el que se tienen en cuenta aspectos tales como las imperfecciones, la posibilidad de incorporar elementos no prismáticos y la caracterización de las uniones semirrígidas, valorando la influencia de su flexibilidad sobre la respuesta de la estructura. Así, se han realizado estudios paramétricos para valorar la sensibilidad y estabilidad de las soluciones obtenidas, así como rangos de validez de las conclusiones obtenidas. This thesis deals with the problems of modelling, analysis and optimization of plane steel frames with regard to ultimate and serviceability limit states. The objective of this work is to present an organized sequential technique of discrete optimization for achieving the minimum cost of plane steel frames, taking into consideration the EC-3 specifications as well as including effects of the semi-rigid joints and non-prismatic elements in the design process. Likewise, an estimate of their influence on the final design is an aim of this work. The final objective is to draw practical conclusions which can be handful and easily applicable for a steel-structure project. An enormous amount of technical and scientific publications regarding steel frames is currently available, thus making the achievement of a comprehensive and updated knowledge a considerably hard task. In this work, a large variety of information has been gathered and classified, especially that related to current research lines and needs. Thus, the literature collected encompasses references related to state-of-the-art design methods, factors influencing the structural response, modelling and optimization techniques, as well as calculation and updated guidelines of some steel Design Codes about the subject. In this work a modelling procedure based on the finite element implemented within the MatLab programming environment has been performed. Several keys aspects have been included, such as second order behaviour, the safety assessment against structural instability and the search for an optimal cost considering the limit states according to EC-3 specifications. The flexibility of joints has been taken into account in the procedure hereby presented; its effects on the structural response, on the optimum weight and on the final cost have also been analysed. In order to confirm the validity and adequacy of this procedure, some application examples have been carried out. The results obtained were compared with those available from other authors. Several conclusions about the procedure that comprises modelling, analysis and design stages, as well as the effect of the flexibility of connections on the structural response have been drawn. The purpose is to point out some guidelines for the early stages of a project. One of the contributions of this thesis is an attempt for optimizing plane steel frames in which both non-prismatic beam-column-type elements and semi-rigid connections have been considered. Thus, an elastic stiffness matrix has been derived. Its validity has been tested through comparing its accuracy with other analytically-obtained matrices available in the literature, and with results obtained by the commercial software SAP2000. Another achievement of this work is the development of a method for cost optimization of plane steel building frames in which some relevant aspects have been taken in consideration. These encompass geometric imperfections, non-prismatic beam elements and the numerical characterization of semi-rigid connections, evaluating the effect of its flexibility on the structural response. Hence, some parametric analyses have been performed in order to assess the sensitivity, the stability of the outcomes and their range of applicability as well.

Discontinuous solutions and boundary value problems for non-linearly elastic fibre-reinforced materials

En este trabajo se han analizado varios problemas en el contexto de la elasticidad no lineal basándose en modelos constitutivos representativos. En particular, se han analizado problemas relacionados con el fenómeno de perdida de estabilidad asociada con condiciones de contorno en el caso de material reforzados con fibras. Cada problema se ha formulado y se ha analizado por separado en diferentes capítulos. En primer lugar se ha mostrado el análisis del gradiente de deformación discontinuo para un material transversalmente isótropo, en particular, el modelo del material considerado consiste de una base neo-Hookeana isótropa incrustada con fibras de refuerzo direccional caracterizadas con un solo parámetro. La solución de este problema se vincula con instabilidades que dan lugar al mecanismo de fallo conocido como banda de cortante. La perdida de elipticidad de las ecuaciones diferenciales de equilibrio es una condición necesaria para que aparezca este tipo de soluciones y por tanto las inestabilidades asociadas. En segundo lugar se ha analizado una deformación combinada de extensión, inación y torsión de un tubo cilíndrico grueso donde se ha encontrado que la deformación citada anteriormente puede ser controlada solo para determinadas direcciones de las fibras refuerzo. Para entender el comportamiento elástico del tubo considerado se ha ilustrado numéricamente los resultados obtenidos para las direcciones admisibles de las fibras de refuerzo bajo la deformación considerada. En tercer lugar se ha estudiado el caso de un tubo cilíndrico grueso reforzado con dos familias de fibras sometido a cortante en la dirección azimutal para un modelo de refuerzo especial. En este problema se ha encontrado que las inestabilidades que aparecen en el material considerado están asociadas con lo que se llama soluciones múltiples de la ecuación diferencial de equilibrio. Se ha encontrado que el fenómeno de instabilidad ocurre en un estado de deformación previo al estado de deformación donde se pierde la elipticidad de la ecuación diferencial de equilibrio. También se ha demostrado que la condición de perdida de elipticidad y ^W=2 = 0 (la segunda derivada de la función de energía con respecto a la deformación) son dos condiciones necesarias para la existencia de soluciones múltiples. Finalmente, se ha analizado detalladamente en el contexto de elipticidad un problema de un tubo cilíndrico grueso sometido a una deformación combinada en las direcciones helicoidal, axial y radial para distintas geotermias de las fibras de refuerzo . In the present work four main problems have been addressed within the framework of non-linear elasticity based on representative constitutive models. Namely, problems related to the loss of stability phenomena associated with boundary value problems for fibre-reinforced materials. Each of the considered problems is formulated and analysed separately in different chapters. We first start with the analysis of discontinuous deformation gradients for a transversely isotropic material under plane deformation. In particular, the material model is an augmented neo-Hookean base with a simple unidirectional reinforcement characterised by a single parameter. The solution of this problem is related to material instabilities and it is associated with a shear band-type failure mode. The loss of ellipticity of the governing differential equations is a necessary condition for the existence of these material instabilities. The second problem involves a detailed analysis of the combined non-linear extension, inflation and torsion of a thick-walled circular cylindrical tube where it has been found that the aforementioned deformation is controllable only for certain preferred directions of transverse isotropy. Numerical results have been illustrated to understand the elastic behaviour of the tube for the admissible preferred directions under the considered deformation. The third problem deals with the analysis of a doubly fibre-reinforced thickwalled circular cylindrical tube undergoing pure azimuthal shear for a special class of the reinforcing model where multiple non-smooth solutions emerge. The associated instability phenomena are found to occur prior to the point where the nominal stress tensor changes monotonicity in a particular direction. It has been also shown that the loss of ellipticity condition that arises from the equilibrium equation and ^W=2 = 0 (the second derivative of the strain-energy function with respect to the deformation) are equivalent necessary conditions for the emergence of multiple solutions for the considered material. Finally, a detailed analysis in the basis of the loss of ellipticity of the governing differential equations for a combined helical, axial and radial elastic deformations of a fibre-reinforced circular cylindrical tube is carried out.

Simulación numérica computacional de fenómenos dinámicos

En este proyecto se trata la simulación numérica de un fenómeno dinámico, basado en el comportamiento de una onda transmitida a lo largo de una cuerda elástica de un instrumento musical, cuyos extremos se encuentran anclados. El fenómeno físico, se desarrolla utilizando una ecuación en derivadas parciales hiperbólicas con variables espacial y temporal, acompañada por unas condiciones de contorno tipo Dirichlet en los extremos y por más condiciones iniciales que dan comienzo al proceso. Posteriormente se han generado algoritmos para el método numérico empleado (Diferencias finitas centrales y progresivas) y la programación del problema aproximado con su consistencia, estabilidad y convergencia, obteniéndose unos resultados acordes con la solución analítica del problema matemático. La programación y salida de resultados se ha realizado con Visual Studio 8.0. y la programación de objetos con Visual Basic .Net In this project the topic is the numerical simulation of a dynamic phenomenon, based on the behavior of a transmitted wave along an elastic string of a musical instrument, whose ends are anchored. The physical phenomenon is developed using a hyperbolic partial differential equation with spatial and temporal variables, accompanied by a Dirichlet boundary conditions at the ends and more initial conditions that start the process. Subsequently generated algorithms for the numerical method used (central and forward finite differences) and the programming of the approximate problem with consistency, stability and convergence, yielding results in line with the analytical solution of the mathematical problem. Programming and output results has been made with Visual Studio 8.0. and object programming with Visual Basic. Net

A dynamic programming approach to the formulation and solution of finite element equations

A method for formulating and algorithmically solving the equations of finite element problems is presented. The method starts with a parametric partition of the domain in juxtaposed strips that permits sweeping the whole region by a sequential addition (or removal) of adjacent strips. The solution of the difference equations constructed over that grid proceeds along with the addition removal of strips in a manner resembling the transfer matrix approach, except that different rules of composition that lead to numerically stable algorithms are used for the stiffness matrices of the strips. Dynamic programming and invariant imbedding ideas underlie the construction of such rules of composition. Among other features of interest, the present methodology provides to some extent the analyst's control over the type and quantity of data to be computed. In particular, the one-sweep method presented in Section 9, with no apparent counterpart in standard methods, appears to be very efficient insofar as time and storage is concerned. The paper ends with the presentation of a numerical example