Parameter uniform optimal order numerical approximations for time-delayed parabolic convection diffusion problems involving two small parameters

DOI10.1007/s40314-022-01928-wOpenAlexW4286628505WikidataQ114219274 ScholiaQ114219274MaRDI QIDQ2167360

S. Priyadarshana, Suvendu Ranjan Pattanaik, Jugal Mohapatra

Publication date: 25 August 2022

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

Full work available at URL: https://doi.org/10.1007/s40314-022-01928-w

zbMATH Keywords

singular perturbationuniform convergenceRichardson extrapolationBakhvalov-Shishkin meshDuran-Shishkin meshtime delay parabolic problem

Mathematics Subject Classification ID

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)

Related Items (6)

A numerical approach for a two-parameter singularly perturbed weakly-coupled system of 2-D elliptic convection-reaction-diffusion PDEs ⋮ An efficient computational technique for time dependent semilinear parabolic problems involving two small parameters ⋮ An improved time accurate numerical estimation for singularly perturbed semilinear parabolic differential equations with small space shifts and a large time lag ⋮ A second order fractional step hybrid numerical algorithm for time delayed singularly perturbed 2D convection-diffusion problems ⋮ Weighted variable based numerical scheme for time-lagged semilinear parabolic problems including small parameter ⋮ Robust numerical schemes for time delayed singularly perturbed parabolic problems with discontinuous convection and source terms

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Numerical solution of singularly perturbed convection-diffusion-reaction problems with two small parameters
• Optimal error estimate using mesh equidistribution technique for singularly perturbed system of reaction-diffusion boundary-value problems
• Comparison of a priori and a posteriori meshes for singularly perturbed nonlinear parameterized problems
• A singularly perturbed problem with two parameters on a Bakhvalov-type mesh
• Richardson extrapolation technique for singularly perturbed parabolic convection--diffusion problems
• A finite difference analysis of a streamline diffusion method on a Shishkin mesh
• Numerical approximations to the scaled first derivatives of the solution to a two parameter singularly perturbed problem
• An upwind difference scheme on a novel Shishkin-type mesh for a linear convection-diffusion problem
• A uniformly convergent scheme on a nonuniform mesh for convection-diffusion parabolic problems
• Uniformly convergent numerical method for singularly perturbed two parameter time delay parabolic problem
• Higher order accurate approximations on equidistributed meshes for boundary layer originated mixed type reaction diffusion systems with multiple scale nature
• A singularly perturbed problem with two parameters in two dimensions on graded meshes
• A fourth-order numerical scheme for singularly perturbed delay parabolic problem arising in population dynamics
• SDFEM for singularly perturbed boundary-value problems with two parameters
• On the approximate solutions of a class of fractional order nonlinear Volterra integro-differential initial value problems and boundary value problems of first kind and their convergence analysis
• A moving mesh refinement based optimal accurate uniformly convergent computational method for a parabolic system of boundary layer originated reaction-diffusion problems with arbitrary small diffusion terms
• A robust numerical method for a two-parameter singularly perturbed time delay parabolic problem
• A numerical method for solving boundary and interior layers dominated parabolic problems with discontinuous convection coefficient and source terms
• An a posteriori based convergence analysis for a nonlinear singularly perturbed system of delay differential equations on an adaptive mesh
• Parameter uniform optimal order numerical approximation of a class of singularly perturbed system of reaction diffusion problems involving a small perturbation parameter
• A uniformly convergent hybrid scheme for singularly perturbed system of reaction-diffusion Robin type boundary-value problems
• Richardson Extrapolation Method for SingularlyPerturbed Convection-Diffusion Problems on AdaptivelyGenerated Mesh
• HIGHER-ORDER PARAMETER UNIFORM CONVERGENT SCHEMES FOR ROBIN TYPE REACTION-DIFFUSION PROBLEMS USING ADAPTIVELY GENERATED GRID
• A Richardson scheme of the decomposition method for solving singularly perturbed parabolic reaction-diffusion equation
• Graded Meshes for Higher Order FEM
• Singularly Perturbed Problems Modeling Reaction-convection-diffusion Processes
• Second-order uniformly convergent numerical method for singularly perturbed delay parabolic partial differential equations
• Numerical treatment of two‐parameter singularly perturbed parabolic convection diffusion problems with non‐smooth data
• Theoretical prospects of fractional order weakly singular Volterra Integro differential equations and their approximations with convergence analysis
• A perturbation-based approach for solving fractional-order Volterra–Fredholm integro differential equations and its convergence analysis
• A parameter-uniform higher order finite difference scheme for singularly perturbed time-dependent parabolic problem with two small parameters
• A graded mesh refinement approach for boundary layer originated singularly perturbed time‐delayed parabolic convection diffusion problems
• A higher order difference method for singularly perturbed parabolic partial differential equations
• Parameter-uniform finite difference schemes for singularly perturbed parabolic diffusion-convection-reaction problems
• On the Asymptotic Solution of a Two-Parameter Boundary Value Problem of Chemical Reactor Theory

This page was built for publication: Parameter uniform optimal order numerical approximations for time-delayed parabolic convection diffusion problems involving two small parameters