Parameter-uniform finite difference method for singularly perturbed parabolic problem with two small parameters

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. The developed method is second-order convergent. Furthermore, the present method produces a more accurate solution than some methods.

Keywords:

• Parameter-uniform
• singularly perturbed
• parabolic problems
• two-parameters
• and accurate solution

Acknowledgments

We thank Jimma University for the necessary support.

Authors’ contributions

All the authors have made substantive contributions to the article and assume full responsibility for its content. These three authors read and approved the final manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).