INVARIANT PRESERVING SCHEMES FOR MULTI-SYMPLECTIC INTEGRATOR IN SHALLOW WATER WAVE PROPAGATION
By
Ram Dayal Pankaja*, Arun Kumarb and Meetha Lal Meenac
aDepartment of Mathematics, J.N.V. University, Jodhpur-342011, Rajasthan India
*Corresponding Author Email:- drrdpankaj@yahoo.com
bDepartment of Mathematics, Government College, Kota-324001, Rajasthan India
Email:- arun.gck@gov.in
cDepartment of Mathematics, Government College, Sawai Madhopur-322021, Rajasthan India
Email:meethalalprince@gmail.com
(Received: December 25, 2020, Revised in format: February 04,2021; Revised In final form : September 24, 2021)
DOI: https://doi.org/10.58250/Jnanabha.2021.51206
Abstract
The concept of discrete conservation of symplecticity for discretizations of Partial Differential Equations (PDEs) for shallow water wave is presented. This property is Endemic and we express that it also leads to exact discrete conservation of momentum and energy for propagation of shallow water wave. This restricted property is stronger than the global property which that synthesis over all spatial framework points leads to distinct symplectic scheme in the time route. Multi-symplectic integrators are earned for propagation of shallow water wave and investigate conservation property for multi-symplectic integrator. Numerical simulations are also offered.
2020 Mathematical Sciences Classification: 37M15, 65P10
Keywords and Phrases: Multi-Symplectic integrators; Shallow water wave; Six Point Scheme