Muhammad Sarfraz Khan, FA16-RMT-022Dr. Yousaf Habib, Assistant Profesor [Supervisor]LHR TP 51892026-04-212018https://repository.cuilahore.edu.pk/123456789/3655The 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.endepartment of mathematicsFA16LHR TP 5189main 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 suitaThesis