Ε-Uniformly convergent numerical scheme for singularly perturbed delay parabolic partial differential equations. Issue 5 (4th May 2017)

• Record Type: Journal Article
• Authors: Gowrisankar, S.; Natesan, Srinivasan
• Is Part Of: International journal of computer mathematics. Volume 94:Issue 5(2017)
• Page Start: 902
• Page End: 921
• Publication Date: 2017-05-04
• Subjects: Singularly perturbed delay parabolic problem -- boundary layer -- piecewise-uniform mesh -- upwind scheme -- uniform convergence; 65M06 -- 65M12 -- CR G1.8; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2016.1154948
• Languages: English
• ISSNs: 0020-7160

Abstract

ABSTRACT: This paper studies the numerical solutions of singularly perturbed parabolic convection–diffusion problems with a delay in time. We divide the domain using a piecewise uniform adaptive mesh in the spatial direction and a uniform mesh in the temporal direction. Further, we discretize the time derivative by the backward-Euler scheme and the spatial derivatives by the upwind finite difference scheme. We obtain the maximum principle and carry out the stability analysis. Then we prove that the proposed scheme isε -uniform convergence of first-order in time and first-order up to a logarithmic factor in space. Numerical results are carried out to verify the theoretical results.