Solution of convection-diffusion problems with singularity using variable mesh spline of third order

Abstract

The paper deals with a third order finite difference approach with variable mesh using the non-polynomial spline for the solution of a problems with singularity in convection-diffusion equation. The problem's discretization equation is constructed using the continuity condition at the inner nodes for the derivatives of first order of the non-polynomial spline, which is not valid at singularity. At the singularity, the problem is modified in order to have a three-term relationship. The method's tridiagonal scheme is interpreted by means of discrete invariant imbedding algorithm. Error analysis of the method is analyzed and the maximum absolute error in the solution is tabulated. Layer behaviour is picturized in graphs.