A Computational Technique for Solving Singularly Perturbed Delay Partial Differential Equations

Abstract

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.

Keywords

• laguerre polynomials and series
• singularly perturbed parabolic problem
• delay partial differential equation
• convergence analysis
• laguerre matrix-collocation method