Numerical Solution of System of Nonlinear Boundary Value Problems Using B Splines

Abstract

This thesis aims to present the numerical solution of a system of nonlinear boundary value problems that have been solved using the variational technique, which includes the Collocation method with B-splines as basis functions and the Galerkin method with B-splines as basis functions. At first, we used the Collocation technique to solve the coupled system of nonlinear boundary value problems. In the Collocation method, the basis functions that constitute a basis for the approximation space under consideration have been redefined into a new set of basis functions matching the number of collocated points chosen in the space variable domain. Next, we used the Galerkin technique to solve the coupled system of nonlinear boundary value problems. In the Galerkin method, the basis functions that constitute a basis for the approximation space under consideration have been redefined into the new set of basis functions which then vanish on the boundary where its Dirichlet type of boundary conditions are specified. The Collocation and Galerkin methods have solved the coupled system of nonlinear boundary value problems with the redefined set of basis functions. The quasilinearization technique has been used to convert a system of nonlinear boundary value problems into a sequence of linear boundary value problems. Some illustrative examples have been considered for testing the efficiency of the proposed Collocation and Galerkin methods. The solutions are then compared to previously existing solutions in the literature. Moreover, to check the accuracy of the solution method, find the residual error analysis. newline