G-Symplectic Partitioned General Linear Methods

Abstract

The main aim of this thesis is to construct structure preserving numerical methods for Hamiltonian systems. General linear methods are a generalization of RK method and LMSM. G symplectic GLM are suitable for numerical integration of Hamiltonian systems in a similar fashion as that of symplectic RK methods. Order 2 G-symplectic general linear methods were constructed by Butcher for numerically preserving Hamiltonian systems having invariants. After that, Order 4 G symplectic general linear methods were constructed. We have constructed order 6 G-symplectic general linear methods that not only preserve energy of Hamiltonian systems but also show zero parasitism.