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Uniformly convergent higher-order finite difference scheme for singularly perturbed parabolic problems with non-smooth data

Bullo Tesfaye Aga, Degla Guy Aymard, Duressa Gemechis File

Journal of Applied Mathematics and Computational Mechanics

2021

Vol. 20, nr 1

5-16

A uniformly convergent higher-order finite difference scheme is constructed and analyzed for solving singularly perturbed parabolic problems with non-smooth data. This scheme involves an average non-standard finite difference with the Richardson extrapolation method for space variables and second-order finite difference approximation for time direction on uniform meshes. The scheme is shown to be second-order convergent in both temporal and spatial directions. Further, the scheme is proven to be uniformly convergent and also confirmed by numerical experiments. Wide numerical experiments are conducted to support the theoretical results and to demonstrate its accuracy. Concisely, the present scheme is stable, convergent, and more accurate than existing methods in the literatur

A Computational Technique for Solving Singularly Perturbed Delay Partial Differential Equations

Gürbüz Burcu

Foundations of Computing and Decision Sciences

2021

Vol. 46, No. 3

221--233

In this work, a matrix method based on Laguerre series to solve singularly perturbed second order delay parabolic convection-diffusion and reaction-diffusion type problems involving boundary and initial conditions is introduced. The approximate solution of the problem is obtained by truncated Laguerre series. Moreover convergence analysis is introduced and stability is explained. Besides, a test case is given and the error analysis is considered by the different norms in order to show the applicability of the method.