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.

A NOTE ON RESOLVENT CONVERGENCE ON A THIN DOMAIN

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

Dressing approach to the nonvanishing boundary value problem for the AKNS hierarchy

We propose an approach to the nonvanishing boundary value problem for integrable hierarchies based on the dressing method. Then we apply the method to the AKNS hierarchy. The solutions are found by introducing appropriate vertex operators that takes into account the boundary conditions.

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.

The influence of zero-value subtraction on the performance of two laser fluorescence devices for detecting occlusal caries in

Background. The aim of this study was to evaluate the influence of zero-value subtraction on the performance of two laser fluorescence (LF) devices developed to 'detect occlusal caries.Methods. The authors selected 119 permanent molars. Two examiners assessed three areas (cuspal, middle and cervical) of both mesial and distal portions of the buccal surface and one occlusal site using an LF device and an LF pen. For each tooth, the authors subtracted the value measured in the cuspal, middle and cervical areas in the buccal surface from the value measured in the respective occlusal site.Results. The authors observed differences among the readings for both devices in the cuspal, middle and cervical areas in the buccal surface as well as differences for both devices with and without the zero-value subtraction in the occlusal surface. When the authors did not perform the zero-value subtraction, they found statistically significant differences for sensitivity and accuracy far the LF device. When this was done with the LF pen, specificity increased and sensitivity decreased significantly.Conclusions. For the LF device, the zero-value subtraction decreased the sensitivity. For this reason, the authors concluded that clinicians can obtain measures with the LF device effectively without using zero-value subtraction. For the LF pen, however, the absence of the zero-value subtraction changed both the Sensitivity and specificity, and so the authors concluded that clinicians should not eliminate this step from the procedure.Clinical Implications. When using the LF device, clinicians might not need to perform the zero-value subtraction; however, for the LF pen, clinicians should do so.

The influence of zero-value subtraction on the performance of two laser fluorescence devices for detecting occlusal caries in vitro

Background. The aim of this study was to evaluate the influence of zero-value subtraction on the performance of two laser fluorescence (LF) devices developed to detect occlusal caries. Methods. The authors selected 119 permanent molars. Two examiners assessed three areas (cuspal, middle and cervical) of both mesial and distal portions of the buccal surface and one occlusal site using an LF device and an LF pen. For each tooth, the authors subtracted the value measured in the cuspal, middle and cervical areas in the buccal surface from the value measured in the respective occlusal site. Results. The authors observed differences among the readings for both devices in the cuspal, middle and cervical areas in the buccal surface as well as differences for both devices with and without the zero-value subtraction in the occlusal surface. When the authors did not perform the zero-value subtraction, they found statistically significant differences for sensitivity and accuracy for the LF device. When this was done with the LF pen, specificity increased and sensitivity decreased significantly. Conclusions. For the LF device, the zero-value subtraction decreased the sensitivity. For this reason, the authors concluded that clinicians can obtain measures with the LF device effectively without using zero-value subtraction. For the LF pen, however, the absence of the zero-value subtraction changed both the sensitivity and specificity, and so the authors concluded that clinicians should not eliminate this step from the procedure. Clinical Implications. When using the LF device, clinicians might not need to perform the zero-value subtraction; however, for the LF pen, clinicians should do so.

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.

Problemas de valor de contorno não clássicos: uma abordagem usando funções de Green

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Funções de Green para problemas de valor de contorno com três pontos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Estrutura algébrica de hierarquias integráveis e problemas de valor de contorno

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Existence of solutions for a class of degenerate quasilinear elliptic equation in R-N with vanishing potentials

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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.

Resolução de problema de valor no contorno associado ao projeto de reatores de fluxo disperso empregados no tratamento de efluentes

The objective of this work was to develop a numerical method to solve boundary value problems concerning to the use of dispersion model for describing the hydraulic behavior of chemical or biological reactors employed in the wastewater treatment. The numerical method was implemented in FORTRAN language generating a computational program which was applied to solve cases involving reaction kinetics of both integer and fractional orders. The developed method was able to solve the proposed problems evidencing to be a useful tool that provides more accurate design of wastewater treatment reactors

Radial sign-changing solutions to biharmonic nonlinear Schrodinger equations

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