A higher order difference method for singularly perturbed parabolic partial differential equations. Issue 3 (4th March 2018)

• Record Type: Journal Article
• Authors: Das, Pratibhamoy
• Is Part Of: Journal of difference equations and applications. Volume 24:Issue 3(2018)
• Page Start: 452
• Page End: 477
• Publication Date: 2018-03-04
• Subjects: Singular perturbation -- boundary layer -- parabolic convection-diffusion problem -- implicit Euler method -- equidistribution principle -- higher order convergence in space and time -- postprocessing methods -- Richardson extrapolation; 65L12 -- 65L50 -- 65M15 -- 35G16 -- 35K20 -- 35K51 -- 65M06 -- 65M50 -- 65M12 -- 65M06 -- 65N12 -- 65N50; Difference equations -- Periodicals; 515.625
• DOI: 10.1080/10236198.2017.1420792
• Languages: English
• ISSNs: 1023-6198

Abstract

Abstract: This paper studies a higher order numerical method for the singularly perturbed parabolic convection-diffusion problems where the diffusion term is multiplied by a small perturbation parameter. In general, the solutions of these type of problems have a boundary layer. Here, we generate a spatial adaptive mesh based on the equidistribution of a positive monitor function. Implicit Euler method is used to discretize the time variable and an upwind scheme is considered in space direction. A higher order convergent solution with respect to space and time is obtained using the postprocessing based extrapolation approach. It is observed that the convergence is independent of perturbation parameter. This technique enhances the order of accuracy from first order uniform convergence to second order uniform convergence in space as well as in time. Comparative study with the existed meshes show the highly effective behavior of the present method.