Efficient approximation of solution derivatives for system of singularly perturbed time-dependent convection-diffusion PDEs on Shishkin mesh

DOI10.1007/S10910-024-01587-8OpenAlexW4392818341MaRDI QIDQ6203919

Kaushik Mukherjee, Sonu Bose

Publication date: 8 April 2024

Published in: Journal of Mathematical Chemistry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10910-024-01587-8

zbMATH Keywords

overlapping boundary layersdiscrete time derivativescaled discrete space derivativestandard Shishkin meshsystem of singularly perturbed convection-diffusion IBVPs

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Finite difference methods for boundary value problems involving PDEs (65N06) Medical epidemiology (92C60)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Parameter-uniform hybrid numerical scheme for time-dependent convection-dominated initial-boundary-value problems
• Analysis of an upwind finite-difference scheme for a system of coupled singularly perturbed convection-diffusion equations
• A uniformly convergent Galerkin method on a Shishkin mesh for a convection-diffusion problem
• Parameter uniform numerical method for a system of two coupled singularly perturbed parabolic convection-diffusion equations
• Numerical analysis of singularly perturbed system of parabolic convection-diffusion problem with regular boundary layers
• A non-uniform difference scheme for solving singularly perturbed 1D-parabolic reaction-convection-diffusion systems with two small parameters and discontinuous source terms
• Richardson extrapolation technique for singularly perturbed system of parabolic partial differential equations with exponential boundary layers
• Numerical approximation of solution derivatives of singularly perturbed parabolic problems of convection-diffusion type
• Difference Methods for Singular Perturbation Problems
• Analysis of Some Difference Approximations for a Singular Perturbation Problem Without Turning Points
• A uniformly convergent numerical method for a coupled system of two singularly perturbed linear reaction-diffusion problems
• Parameter-uniform finite difference scheme for a system of coupled singularly perturbed convection–diffusion equations
• A finite-difference scheme for a coupled system of singularly perturbed time-dependent reaction–diffusion equations with discontinuous source terms
• Approximation of derivative to a singularly perturbed second-order ordinary differential equation with discontinuous convection coefficient using hybrid difference scheme
• UNIFORMLY-CONVERGENT NUMERICAL METHODS FOR A SYSTEM OF COUPLED SINGULARLY PERTURBED CONVECTION–DIFFUSION EQUATIONS WITH MIXED TYPE BOUNDARY CONDITIONS
• Approximation of derivatives in a convection-diffusion two-point boundary value problem
• Approximation of derivative in a system of singularly perturbed convection-diffusion equations
• A fast uniformly accurate global numerical approximation to solution and scaled derivative of system of singularly perturbed problems with multiple diffusion parameters on generalized adaptive mesh

This page was built for publication: Efficient approximation of solution derivatives for system of singularly perturbed time-dependent convection-diffusion PDEs on Shishkin mesh