A modification of the Shishkin discretization mesh for one-dimensional reaction-diffusion problems

DOI10.1016/j.amc.2013.05.055zbMath1329.65168OpenAlexW2047131285MaRDI QIDQ902481

Relja Vulanović, Ljiljana Teofanov

Publication date: 18 January 2016

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

Full work available at URL: https://doi.org/10.1016/j.amc.2013.05.055

zbMATH Keywords

singular perturbationuniform convergencefinite differencesboundary value problemShishkin mesh

Mathematics Subject Classification ID

Numerical solution of boundary value problems involving ordinary differential equations (65L10) 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)

An a priori harmonic mesh for singularly perturbed boundary value problems ⋮ A modified graded mesh and higher order finite element method for singularly perturbed reaction-diffusion problems ⋮ On the quasilinear boundary-layer problem and its numerical solution ⋮ Numerical treatment of a quasilinear initial value problem with boundary layer ⋮ A modified graded mesh and higher order finite element approximation for singular perturbation problems ⋮ Rational spectral collocation and differential evolution algorithms for singularly perturbed problems with an interior layer ⋮ An improved extrapolated collocation technique for singularly perturbed problems using cubic B-spline functions ⋮ A robust adaptive grid method for a nonlinear singularly perturbed differential equation with integral boundary condition

Cites Work

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• A brief survey on numerical methods for solving singularly perturbed problems
• High order parameter-robust numerical method for singularly perturbed reaction-diffusion problems
• Robust convergence of a compact fourth-order finite difference scheme for reaction-diffusion problems
• Layer-adapted meshes for reaction-convection-diffusion problems
• On the rate of convergence, uniform with respect to a small parameter, of a difference scheme for an ordinary differential equation
• A priori meshes for singularly perturbed quasilinear two-point boundary value problems
• Robust Numerical Methods for Singularly Perturbed Differential Equations
• Analysis of Some Difference Approximations for a Singular Perturbation Problem Without Turning Points
• Uniform Pointwise Convergence on Shishkin-Type Meshes for Quasi-Linear Convection-Diffusion Problems
• On a uniformly accurate finite difference approximation of a singularly perturbed reaction-diffusion problem using grid equidistribution
• A higher-order scheme for quasilinear boundary value problems with two small parameters

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