On the Construction of Higher Order Conservative Methods

Abstract

For the numerical solution of conservative differential equations such as Hamiltonian system or differential equations that arise in different physical phenomena with some structure, we use structure preserving numerical methods. In particular, symplectic Runge-Kutta methods, G-symplectic General Linear methods and Variational Integrators have been explored. In this thesis Variational Integrators for degenerate Lagrangian and non- degenerate Lagrangian have been discussed. For degenerate Lagrangian, we obtain multi-step numerical methods which suffer from parasitic corruption. In order to control the parasitism we write Variational Integrators as General Linear methods and then employ the projection technique to project the numerical solution onto the desired manifold