A special numerical method for solving Hamiltonian eigenproblems

In this thesis we develop and implement a new algorithm for finding the solutions of linear Hamiltonian systems arising from ordinary differential equation (ODE) eigenproblems; a large source of these systems is Sturm-Liouville problems, and these will provide the angle of approach. The convergence properties of the algorithm will be analysed, as will the performance of the algorithm for large values of eigenparameter.;An algorithm is also proposed to find high-index eigenvalues of general Sturm-Liouville problems.