Alternating direction numerical scheme for singularly perturbed 2D degenerate parabolic convection-diffusion problems

DOI10.1016/j.amc.2017.06.010zbMath1427.65176OpenAlexW2724326517MaRDI QIDQ1740071

Anirban Majumdar, Srinivasan Natesan

Publication date: 29 April 2019

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

Full work available at URL: https://doi.org/10.1016/j.amc.2017.06.010

zbMATH Keywords

uniform convergencefinite difference schemepiecewise-uniform Shishkin meshesalternating direction schemesingularly perturbed 2D degenerate parabolic convection-diffusion problem

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Initial-boundary value problems for second-order parabolic equations (35K20) 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 the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22)

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Cites Work

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• A parallel boundary value technique for singularly perturbed two-point boundary value problems
• A lower bound for the smallest singular value of a matrix
• Initial-value technique for singularly-perturbed turning-point problems exhibiting twin boundary layers
• A computational method for solving singularly perturbed turning point problems exhibiting twin boundary layers
• A fractional step method on a special mesh for the resolution of multidimensional evolutionary convection-diffusion problems
• Parameter uniform numerical method for singularly perturbed turning point problems exhibiting boundary layers.
• A numerical algorithm for singular perturbation problems exhibiting weak boundary layers.
• Numerical solution of nonlinear singularly perturbed problems on nonuniform meshes by using a non-standard algorithm
• An efficient numerical method for singular perturbation problems
• A high order uniformly convergent alternating direction scheme for time dependent reaction-diffusion singularly perturbed problems
• Continuous and Numerical Analysis of a Multiple Boundary Turning Point Problem
• Robust Numerical Methods for Singularly Perturbed Differential Equations
• A Fitted Mesh Method for a Class of Singularly Perturbed Parabolic Problems with a Boundary Turning Point
• An alternating direction scheme on a nonuniform mesh for reaction-diffusion parabolic problems
• A robust finite difference method for a singularly perturbed degenerate parabolic problem II
• CONSERVATIVE NUMERICAL METHOD FOR A SYSTEM OF SEMILINEAR SINGULARLY PERTURBED PARABOLIC REACTION‐DIFFUSION EQUATIONS