An Elementary Introduction to Recently Developed Computational Methods for Solving Singularly Perturbed Partial Differential Equations Arising in Science and Engineering

Abstract

This paper presents a survey of innovative approaches of the most effective computational techniques for solving singular perturbed partial differential equations, which are useful because of their numerical and computer realizations. Many applied problems appearing in semiconductors theory, biochemistry, kinetics, theory of electrical chains, economics, solid mechanics, fluid dynamics, quantum mechanics, and many others can be modelled as singularly perturbed systems. Here, we summarize a wide range of research articles published by numerous researchers during the last ten years to get a better view of the present scenario in this area of research.

Keywords:

• Singular perturbations
• Reaction-diffusion
• Convection Diffusion
• Boundary layer
• Interior layer
• Asymptotic analysis

Acknowledgments

The authors extend their appreciation to anonymous reviewers for their valuable suggestions for revising this paper.