A finite differences MATLAB code for the numerical solution of second order singular perturbation problems

Authors:
Pierluigi Amodio;Giuseppina Settanni
Affiliations:
-;-
Venue:
Journal of Computational and Applied Mathematics
Year:
2012

Citing 9
Cited 0

A new basis implementation for a mixed order boundary value ODE solver

SIAM Journal on Scientific and Statistical Computing
A deferred correction method for nonlinear two-point boundary value problems: implementation and numerical evaluation

SIAM Journal on Scientific and Statistical Computing
An automatic continuation strategy for the solution of singularly perturbed linear two-point boundary value problems

Journal of Computational Physics
Convergence and stability of boundary value methods for ordinary differential equations

Proceedings of the 6th international congress on Computational and applied mathematics
Algorithm 569: COLSYS: Collocation Software for Boundary-Value ODEs [D2]

ACM Transactions on Mathematical Software (TOMS)
An automatic continuation strategy for the solution of singularly perturbed nonlinear boundary value problems

ACM Transactions on Mathematical Software (TOMS)
Numerical approximation of nonlinear BVPs by means of BVMs

Applied Numerical Mathematics
A new mesh selection algorithm, based on conditioning, for two-point boundary value codes

Journal of Computational and Applied Mathematics
High-order finite difference schemes for the solution of second-order BVPs

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	7.29

Visualization

Abstract

We show the main features of the MATLAB code HOFiD_UP for solving second order singular perturbation problems. The code is based on high order finite differences, in particular on the generalized upwind method. Within its simplicity, it uses order variation and continuation for solving any difficult nonlinear scalar problem. Several numerical tests on linear and nonlinear problems are considered. The best performances are reported on problems with perturbation parameters near the machine precision, where most of the codes for two-point BVPs fail.