An exponentially-fitted method for singularly perturbed, one-dimensional, parabolic problems

DOI10.1016/j.amc.2003.12.046zbMath1061.65089OpenAlexW2154272663MaRDI QIDQ1763315

Juan I. Ramos

Publication date: 22 February 2005

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

Full work available at URL: https://doi.org/10.1016/j.amc.2003.12.046

zbMATH Keywords

numerical examplessemidiscretizationupwind finite difference schemeboundary-layerParabolic equationsAdvection-reaction-diffusion equationsconvergence comparison of methodsExponentially-fitted methodSingularly perturbations

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Initial value problems for second-order parabolic equations (35K15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items

Numerical solution of singularly perturbed convection-diffusion-reaction problems with two small parameters ⋮ Reproducing kernel method for singularly perturbed one-dimensional initial-boundary value problems with exponential initial layers ⋮ Fitted numerical methods for singularly perturbed one-dimensional parabolic partial differential equations with small shifts arising in the modelling of neuronal variability ⋮ Application of sinc-Galerkin method to singularly perturbed parabolic convection-diffusion problems ⋮ A brief survey on numerical methods for solving singularly perturbed problems ⋮ Computational method for singularly perturbed two-parameter parabolic convection-diffusion problems ⋮ A uniformly convergent B-spline collocation method on a nonuniform mesh for singularly perturbed one-dimensional time-dependent linear convection-diffusion problem ⋮ A fitted operator finite difference method of lines for singularly perturbed parabolic convection-diffusion problems ⋮ An exponentially fitted method for solving Burgers' equation ⋮ A quintic spline collocation method for solving time-dependent convection-diffusion problems ⋮ Exponentially-fitted methods on layer-adapted meshes ⋮ Unnamed Item

Cites Work

• Singular perturbation methods for ordinary differential equations
• On diffusive methods and exponentially fitted techniques
• Ten ways to generate the Il'in and related schemes
• Special meshes for finite difference approximations to an advection- diffusion equation with parabolic layers
• Modelling nonlocal processes in semiconductor devices with exponential difference schemes
• A uniformly convergent scheme on a nonuniform mesh for convection-diffusion parabolic problems
• The \(hp\) finite element method for problems in mechanics with boundary layers
• Numerical method for boundary layers with blowing - The exponential box scheme
• RELAXATION METHODS APPLIED TO DETERMINE THE MOTION, IN TWO DIMENSIONS, OF A VISCOUS FLUID PAST A FIXED CYLINDER
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item