Numerical solutions of linear and nonlinear eigenvalue problems using Taylor's decomposition method

The main purpose of this thesis is to solve regular Sturm-Liouville eigenvalue problems and some special nonlinear eigenvalue problems numerically using Taylor?s decomposition method. The numerical scheme is based on the application of the Taylor?s decomposition to the corresponding first order differential equation system. The technique is illustrated with three problems, regular Sturm-Liouville eigenvalueproblems, Bratu problem and Euler buckling problem. The results show that the method converges rapidly and hence approximates the exact solution very accurately for relatively large step-sizes.