ANTHONY COLLINS OGBEIDE

Brief history, origin and relevant roles of some numerical methods in the solution of the Hamiltonian Differential Equation with the help of some definitions and theorem. Some important results, are incorporated in this work, extending, specifically the Runge-Kutta Methods. We study the application of Runge-Kutta schemes to Hamiltonian systems. Basic principles are illustrated by means of examples. This work has been selected carefully so that the work is useful for study in this area of research. Particularly, a survey of the effectiveness of the Runge-kutta Methods. The numerical methods developed are primarily intended for use with Hamiltonian systems, but many find uses in solving other forms of ordinary differential equations. Almost all the real conservative physical processes can be cast in suitable Hamiltonian formulation in phase spaces with symplectic structure, which has the advantages to make the intrinsic properties and symmetries of the underlying processes more explicit than in other mathematically equivalent formulations, so I choose the Hamiltonian formalism as the basis, together with the mathematical and physical motivations of our symplectic approach for the purpose of numerical simulation of dynamical evolutions.

Brief history, origin and relevant roles of some numerical methods in the solution of the Hamiltonian Differential Equation with the help of some definitions and theorem. Some important results, are incorporated in this work, extending, specifically the Runge-Kutta Methods. We study the application of Runge-Kutta schemes to Hamiltonian systems. Basic principles are illustrated by means of examples. This work has been selected carefully so that the work is useful for study in this area of research. Particularly, a survey of the effectiveness of the Runge-kutta Methods. The numerical methods developed are primarily intended for use with Hamiltonian systems, but many find uses in solving other forms of ordinary differential equations. Almost all the real conservative physical processes can be cast in suitable Hamiltonian formulation in phase spaces with symplectic structure, which has the advantages to make the intrinsic properties and symmetries of the underlying processes more explicit than in other mathematically equivalent formulations, so I choose the Hamiltonian formalism as the basis, together with the mathematical and physical motivations of our symplectic approach for the purpose of numerical simulation of dynamical evolutions.