Lobatto deferred correction for stiff two-point boundary value problems

An iterated deferred correction algorithm based on Lobatto Runge-Kutta formulae is developed for the efficient numerical solution of nonlinear stiff two-point boundary value problems. An analysis of the stability properties of general deferred correction schemes which are based on implicit Runge-Kutta methods is given and results which are analogous to those obtained for initial value problems are derived. A revised definition of symmetry is presented and this ensures that each deferred correction produces an optimal increase in order. Finally, some numerical results are given to demonstrate the superior performance of Lobatto formulae compared with mono-implicit formulae on stiff two-point boundary value problems. (C) 1998 Elsevier B.V. Ltd. All rights reserved.

Iterated deferred correction for linear two-point boundary value problems

An analysis of iterated deferred correction based on various classes of implicit Runge-Kutta formulae is given. Out of different possibilities considered, it is shown that those based purely on Lobatto formulae have the best stability. The enhanced stability of Lobatto schemes is very important for the efficient integration of excessively stiff boundary value problems and this is demonstrated by means of some numerical results.

Chawla-Numerov method revisited

The well-known two-step fourth-order Numerov method was shown to have better interval of periodicity when made explicit, see Chawla (1984). It is readily verifiable that the improved method still has phase-lag of order 4. We suggest a slight modification from which linear problems could benefit. Phase-lag of any order can be achieved, but only order 6 is derived. © 1991.

Desenvolvimento da função perturbadora e aplicações em dinâmica de exoplanetas

Pós-graduação em Matemática Universitária - IGCE

Métodos numéricos para equações diferencias ordinárias

Pós-graduação em Matemática Universitária - IGCE

Initial-condition problem for a chiral Gross-Neveu system

A time-dependent projection technique is used to treat the initial-value problem for self-interacting fermionic fields. On the basis of the general dynamics of the fields, we derive formal equations of kinetic-type for the set of one-body dynamical variables. A nonperturbative mean-field expansion can be written for these equations. We treat this expansion in lowest order, which corresponds to the Gaussian mean-field approximation, for a uniform system described by the chiral Gross-Neveu Hamiltonian. Standard stationary features of the model, such as dynamical mass generation due to chiral symmetry breaking and a phenomenon analogous to dimensional transmutation, are reobtained in this context. The mean-field time evolution of nonequilibrium initial states is discussed.

One-sided and two-sided Green's functions

We discuss the one-sided Green's function, associated with an initial value problem and the two-sided Green's function related to a boundary value problem. We present a specific calculation associated with a differential equation with constant coefficients. For both problems, we also present the Laplace integral transform as another methodology to calculate these Green's functions and conclude which is the most convenient one. An incursion in the so-called fractional Green's function is also presented. As an example, we discuss the isotropic harmonic oscillator.

Taxas de decomposição e de liberação de macronutrientes da palhada de aveia preta em plantio direto

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Study of Monoethanolamine Nitrate Content Reduction in Explosive Slurries

The reduction of the fuel content of a monoethanolamine nitrate (MEAN) fueled explosive slurry was investigated. The work was performed in three phases. The first one involved the MEAN content reduction in a reference slurry from its initial value of 36 down to 24% by weight, the balance being filled with ammonium nitrate, the least expensive item in the slurry composition. This proved to be successful, leading to an overall cost reduction of 17%, while keeping the overall performance quite satisfactory. The second phase consisted in trying to bring the MEAN content down from 24 to 17%. Although this led to further cost reduction, the formulations, obtained by substituting part of the MEAN content by ammonium nitrate/fuel oil (ANFO), produced unsatisfactory results regarding ignition and densities. In the third phase, the Design of Experiments Technique was used to find formulations displaying not only lower cost, but also acceptable overall performance. This led to a raw material cost reduction ranging from 23 to 26% relative to the initial reference slurry formulation.

Renormalized coordinate approach to the thermalization process

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Usando um voltímetro para medir tempo

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Metodologia experimental para avaliação de custos de produção e utilização de biodiesel: estudo de caso de quatro ésteres metílicos e óleo diesel comercial

Considerando que o Brasil detém uma vasta gama de matérias-primas para produção de biodiesel, e também que há a possibilidade de produção em pequena escala, prima-se por estudos de cunho econômico a partir de metodologias de fácil execução. O objetivo do trabalho foi demonstrar uma metodologia e sua aplicação para avaliação dos custos inseridos dentro do processo produtivo e de utilização do biodiesel. A metodologia foi aplicada a biodieseis originários de óleo de soja, girassol, frango e sebo bovino, dos quais se avaliaram economicamente os custos fixos e variáveis para conversão química dos óleos e gorduras em ésteres metílicos, em uma planta de produção experimental. Os custos de produção para cada uma das quatro citadas são distintos em função do valor inicial por litro de cada uma. Também fora avaliado o custo específico e o consumo específico de cada um dos biodieseis, a fim de determinar a diferença em relação ao óleo diesel comercial. No estudo de caso, os resultados mostraram vantagens para o óleo diesel, tanto no custo quanto no consumo. Comparando-se os biodieseis, o de sebo bovino apresentou-se com o menor custo de produção e o menor consumo.

Interpolating EFGM for computing continuous and discontinuous electromagnetic fields

Purpose - This paper proposes an interpolating approach of the element-free Galerkin method (EFGM) coupled with a modified truncation scheme for solving Poisson's boundary value problems in domains involving material non-homogeneities. The suitability and efficiency of the proposed implementation are evaluated for a given set of test cases of electrostatic field in domains involving different material interfaces.Design/methodology/approach - the authors combined an interpolating approximation with a modified domain truncation scheme, which avoids additional techniques for enforcing the Dirichlet boundary conditions and for dealing with material interfaces usually employed in meshfree formulations.Findings - the local electric potential and field distributions were correctly described as well as the global quantities like the total potency and resistance. Since, the treatment of the material interfaces becomes practically the same for both the finite element method (FEM) and the proposed EFGM, FEM-oriented programs can, thus, be easily extended to provide EFGM approximations.Research limitations/implications - the robustness of the proposed formulation became evident from the error analyses of the local and global variables, including in the case of high-material discontinuity.Practical implications - the proposed approach has shown to be as robust as linear FEM. Thus, it becomes an attractive alternative, also because it avoids the use of additional techniques to deal with boundary/interface conditions commonly employed in meshfree formulations.Originality/value - This paper reintroduces the domain truncation in the EFGM context, but by using a set of interpolating shape functions the authors avoided the use of Lagrange multipliers as well Mathematics in Engineering high-material discontinuity.

An application of the Adomian's decomposition method to the analysis of MHD duct flows

A new approach is proposed in this work for the treatment of boundary value problems through the Adomian's decomposition method. Although frequently claimed as accurate and having fast convergence rates, the original formulation of Adomian's method does not allow the treatment of homogeneous boundary conditions along closed boundaries. The technique here presented overcomes this difficulty, and is applied to the analysis of magnetohydrodynamic duct flows. Results are in good agreement with finite element method calculations and analytical solutions for square ducts. Therefore, new possibilities appear for the application of Adomian's method in electromagnetics.

Dielectric and fatigue properties of Pb(Zr0.53Ti0.47)O-3 thin films prepared from oxide precursors method

Fatigue is an important problem to be considered if a ferroelectric film is used for non-volatile memory devices. In this phenomena, the remanent polarization and coercive field properties degrades in cycles which increase in hysteresis loops. The reasons have been attributed to different mechanisms such as a large voltage applied on ferroelectric film in every reading process in Ferroelectric Random Access Memory (FeRAM) or memories for digital storage in computer, grain size effects and others. The aim of this work is to investigate the influence of the crystallization kinetics on dielectric and ferroelectric properties of the Pb(Zr0.53Ti0.47)O-3 thin films prepared by an alternative chemical method. Films were crystallized in air on Pt/Ti/SiO2/Si substrates at 700 degrees C for 1 hour, in conventional thermal annealing (CTA), and at 700 degrees C for 1 min and 700 degrees C 5 min, using a rapid thermal annealing (RTA) process. Final films were crack free and presented an average of 750 nm in thickness. Dielectric properties were studied in the frequency range of 100 Hz - 1 MHz. All films showed a dielectric dispersion at low frequency. Ferroelectric properties were measured from hysteresis loops at 10 kHz. The obtained remanent polarization (P-r) and coercive field (E-c) were 3.7 mu C/cm(2) and 71.9 kV/cm respectively for film crystallized by CTA while in films crystallized by RTA these parameters were essentially the same. In the fatigue process, the P, value decreased to 14% from the initial value after 1.3 x 10(9) switching cycles, for film by CTA, while for film crystallized by RTA for 5 min, P, decreased to 47% from initial value after 1.7 x 10(9) switching cycles.