Computer assisted analytical and numerical methods of solving linear and non linear boundary value problems

Abstract

Boundary value problems (BVPs) and Eigen boundary value problems (EBVPs) occur quite frequently in many practical problems of interest in several disciplines. Compared to the methods of solving initial value problems there are not many satisfactory methods of solving BVPs and EBVPs. Convergence is an issue while using many numerical methods for these problems. A scientific approach needs to be adopted in order to make the right choices of quantities that are needed to make the numerical methods work well. The objective of the thesis is, therefore, to propose ways and means of ensuring correct numerical results while solving BVPs and EBVPs. This is achieved through a combination of methods and through a scientific choice of initial approximations needed to get the numerical method work well to obtain results with the desired accuracy. newline