Browsing by Author "Sabawe, Bahaa Ahmed Khalaf"
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Item AVERAGE VECTOR FIELD METHOD FOR HAMILTONIAN SYSTEMS(2022-01-11) Sabawe, Bahaa Ahmed Khalaf; Aydın, AyhanIn this thesis, we present and analyze four energy preserving methods for the numer ical solution of initial value problems of Hamiltonian type. In particular, the average vector field (AVF) and partitioned AVF (PAVF) methods are used to drive energy preserving methods. In addition to these two energy preserving methods, two en ergy persevering PAVF composition (PAVF-C) and PAVF plus (AVF-P) methods are presented. The thesis accompanied numerical result for Zakharov system that demon strate remarkable properties of the proposed energy persevering methods. In this the sis, this is the first time that energy persevering AVF, PAVF, PAVF-C and PAVF-P methods are proposed for Zakharov system. It is shown that PAVF and PAVF-C meth ods for Zakharov system are linearly implicit methods that have remarkable lower cost than the original AVF method. In addition, we further show that the PAVF meth ods preserve the mass conservation of the Zakharov system while the AVF method cannot.