Computational technique for two parameter singularly perturbed parabolic convection-diffusion problem

Abstract

We study the singularly perturbed parabolic differential equation of convection-diffusion type with two small parameters affecting the derivatives. Using backward Euler process, time discretization is achieved. Problem is discretized in space using two fitting factors on uniform mesh where these factors take care of the two small parameters. Numerical scheme is constructed using two parameter fitting method. Tridiagonal solver is used to solve the resulting system of equations. Numerical results justify the parameter-uniform convergence of the scheme. We also mull numerical examples in comparing with remaining methods in the literature to uphold the method.