Numerical solution of stiff and convection-diffusion equations using adaptive spline function approximation

The singular perturbation mathematical model plays an important role in modelling fluid processes which arise in applied mechanics. We have either, the stiff system of initial value problems or convection-diffusion problems. When conventional numerical methods are used to obtain the solution, the stepsize must be limited to small values. Any attempt to use a larger step-size results in the production of nonphysical oscillations in the solution.In this paper we have constructed an adaptive spline function to solve initial and boundary value problems of ordinary and partial differential equations. The numerical methods based on the spline relations when applied to the test models produce oscillation free solutions. The numerical results are presented and discussed.