A numerical method for a nonlinear singularly perturbed interior layer problem using an approximate layer location

DOI10.1016/j.cam.2015.06.009zbMath1321.65121OpenAlexW1580867777MaRDI QIDQ492126

Jason Quinn

Publication date: 19 August 2015

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2015.06.009

zbMATH Keywords

convergencesingularly perturbed problemnonlinearShishkin meshnumerical experimentinterior layer

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Singular perturbations for ordinary differential equations (34E15) Finite difference and finite volume methods for ordinary differential equations (65L12) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50) Numerical solution of singularly perturbed problems involving ordinary differential equations (65L11)

Related Items (8)

Numerical simulation of front dynamics in a nonlinear singularly perturbed reaction-diffusion problem ⋮ Some features of solving an inverse backward problem for a generalized Burgers' equation ⋮ Rational spectral collocation and differential evolution algorithms for singularly perturbed problems with an interior layer ⋮ Quintic B-spline method for solving second order linear and nonlinear singularly perturbed two-point boundary value problems ⋮ Solution with an inner transition layer of a two-dimensional boundary value reaction-diffusion-advection problem with discontinuous reaction and advection terms ⋮ An adaptive difference scheme for parabolic delay differential equation with discontinuous coefficients and interior layers ⋮ Development of methods of asymptotic analysis of transition layers in reaction-diffusion-advection equations: theory and applications ⋮ Analytical-numerical approach to describing time-periodic motion of fronts in singularly perturbed reaction-advection-diffusion models

Cites Work

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• A Shishkin mesh for a singularly perturbed Riccati equation
• Parameter-uniform numerical methods for some linear and nonlinear singularly perturbed convection diffusion boundary turning point problems
• Stabilised approximation of interior-layer solutions of a singularly perturbed semilinear reaction-diffusion problem
• An introduction to nonlinear boundary value problems
• Step-like contrasting structures for a singularly perturbed quasilinear second-order differential equation
• Existence and asymptotic stability of periodic solutions with an interior layer of reaction-advection-diffusion equations
• Periodic step-like contrast structures for a singularly perturbed parabolic equation

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