A Higher Order Finite Difference Method for a Singularly Perturbed Boundary Value Problem with a Small Negative Shift

This study proposes a uniformly convergent finite difference scheme on a uniform mesh to solve singularly perturbed boundary value problems for second-order ordinary differential-difference equation of the convection-diffusion type. Error estimates are produced for the proposed numerical scheme. The...

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Bibliographic Details
Published in:International journal of applied and computational mathematics 2023-10, Vol.9 (5), Article 101
Main Authors: Prathap, T., Rao, R. Nageshwar
Format: Article
Language:English
Subjects:
Applications of Mathematics
Applied mathematics
Boundary value problems
Computational mathematics
Computational Science and Engineering
Convection-diffusion equation
Difference equations
Differential equations
Finite difference method
Finite element method
Mathematical analysis
Mathematical and Computational Physics
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Nuclear Energy
Operations Research/Decision Theory
Original Paper
Singular perturbation methods
Theoretical
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Description
Summary:This study proposes a uniformly convergent finite difference scheme on a uniform mesh to solve singularly perturbed boundary value problems for second-order ordinary differential-difference equation of the convection-diffusion type. Error estimates are produced for the proposed numerical scheme. The theoretical results are supported by numerical simulations of test problems.
ISSN:2349-5103
2199-5796
DOI:10.1007/s40819-023-01578-4