# A parameter-uniform finite difference scheme for singularly perturbed parabolic problem with two small parameters

## DOI:

https://doi.org/10.13052/ejcm2642-2085.30233## Keywords:

Parameter-uniform, singularly perturbed, parabolic problems, two-parameters, finite difference scheme, error bounds, and accurate solution.## Abstract

A parameter-uniform finite difference scheme is constructed and analyzed for solving singularly perturbed parabolic problems with two parameters. The solution involves boundary layers at both the left and right ends of the solution domain. A numerical algorithm is formulated based on uniform mesh finite difference approximation for time variable and appropriate piecewise uniform mesh for the spatial variable. Parameter-uniform error bounds are established for both theoretical and experimental results and observed that the scheme is second-order convergent. Furthermore, the present method produces a more accurate solution than some methods existing in the literature.

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