Solution of Time-Dependent Linear Singular Perturbation Problems Using Collocation Techniques with Hermite Basis

Time-dependent singular perturbation problems having steep gradients near boundary are solved numerically, using the Hermite collocation method. Cubic Hermite polynomials have been taken as interpolating polynomials with two collocation points within each mesh [x_i–1, x_i] where, i = 1, 2,…, n. Parameter uniform convergence has been carried out using the technique given by Farrell and Hegarty (Farrell, P.A., Hegarty, A., 1991. On the Determination of the Order of Uniform Convergence. In Proceedings of the13th World Congress on Computation and Applied Mathematics, 2, pp. B1–B2). Hermite collocation is applied on different singular perturbation problems. Numerical results are presented in terms of 2D and 3D graphs to analyse the problems. The rate of convergence of Hermite collocation method is found to be dependent on the mesh points. The point wise error and rate of convergence are presented in tabular form.