Non-Polynomial Cubic Spline Method for solving Singularly Perturbed Delay ConvectionDiffusion Equations

Abstract

In this thesis, non-polynomial cubic spline method is presented for solving singularly perturbed delay convection diffusion equations . First the second order singularly perturbed delay convection diffusion equation transformed in to an asymptotically equivalent singularly perturbed boundary value problem. Then non-polynomial cubic spline approximations are changed in to a three-term recurrence relation, which can be solved using Thomas Algorithm. The stability and convergence of the method have been established. The applicability of the proposed method is validated by implementing it by four model examples with different values of perturbation parameter  , delay parameter and mesh size h. The numerical results have been presented in tables and further to examine the effect of delay on the left and right boundary layer of the solution; graphs have been given for different values of .  To show the accuracy of the method, the results are presented in terms of maximum absolute errors. Concisely, the present method gives more accuracy result than some existing numerical methods reported in the literature.