Quadratic B-spline Collocation Method for Solving Singularly Perturbed Quasilinear Sobolev Equations

Abstract

In this thesis, the one-dimensional singularly perturbed quasilinear Sobolev equationis considered and treated numerically. Newton’s linearization approach is used to linearize the nonlinear term. The finite difference method is used to treat the linearized equation spatial direction discretization. The temporal direction the quadratic B-spline collocation method is applied. The propsed scheme’s stability is analysed and established. The scheme converges with an order of convergence one in time and two in space. The theoretical results were illustrated using numerical example.