A second-order difference scheme for a parameterized singular perturbation problem

DOI10.1016/j.cam.2007.10.004zbMath1154.65064OpenAlexW2041027666MaRDI QIDQ950088

Zhongdi Cen

Publication date: 22 October 2008

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.2007.10.004

zbMATH Keywords

uniform convergencenumerical experimentsShishkin meshesSingular perturbationquasilinear boundary value problemmidpoint difference schemeparametrized problem

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) 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)

Related Items (17)

Parameter-uniform numerical methods for a class of parameterized singular perturbation problems ⋮ Exponential fitted operator method for singularly perturbed convection-diffusion type problems with nonlocal boundary condition ⋮ A second order uniformly convergent numerical scheme for parameterized singularly perturbed delay differential problems ⋮ A brief survey on numerical methods for solving singularly perturbed problems ⋮ Fitted second order numerical method for a singularly perturbed Fredholm integro-differential equation ⋮ Method of exact difference schemes for the numerical solution of parameterized singularly perturbed problem ⋮ Analytic approximate solutions of parameterized unperturbed and singularly perturbed boundary value problems ⋮ Uniformly convergent second order numerical method for a class of parameterized singular perturbation problems ⋮ A parameter uniform difference scheme for the parameterized singularly perturbed problem with integral boundary condition ⋮ An almost second order uniformly convergent scheme for a singularly perturbed initial value problem ⋮ An improved a posteriori error estimation for a parameterized singular perturbation problem ⋮ Comparison of a priori and a posteriori meshes for singularly perturbed nonlinear parameterized problems ⋮ A fitted second-order difference method for a parameterized problem with integral boundary condition exhibiting initial layer ⋮ A second order accurate method for a parameterized singularly perturbed problem with integral boundary condition ⋮ A posteriori error estimation for quasilinear singularly perturbed problems with integral boundary condition ⋮ A higher order difference method for singularly perturbed parabolic partial differential equations ⋮ A novel second-order fitted computational method for a singularly perturbed Volterra integro-differential equation

Cites Work

• A note on a parameterized singular perturbation problem
• Singular perturbation methods for ordinary differential equations
• Parametrized singularly perturbed boundary value problems
• The midpoint upwind scheme
• Layer-adapted meshes for convection-diffusion problems
• Analysis of Some Difference Approximations for a Singular Perturbation Problem Without Turning Points
• A Constructive Theorem of Existence and Uniqueness for the Problem\documentclass{article}\pagestyle{empty}\begin{document}$ y' = f(x,y,\lambda),y(a) = \alpha,y\left( b\right) = \beta $\end{document}
• Sufficient conditions for uniform convergence on layer-adapted grids
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: A second-order difference scheme for a parameterized singular perturbation problem