An energy-preserving computational approach for the semilinear space fractional damped Klein–Gordon equation with a generalized scalar potential
Hendy A.S. Taha T.R. Suragan D. Zaky M.A.
August 2022Elsevier Inc.
Applied Mathematical Modelling
2022#108512 - 530 pp.
Naturally preserving dissipative or conservative structures of a given continuous system in discrete analogs is of high demand when designing numerical schemes for dissipative or Hamiltonian partial differential equations. Armed with this fact, the proposed computational study focuses on the issue of considering energy-preserving discrete numerical schemes for the Riesz space-fractional Klein-Gordon equation with a generalized scalar potential. For the sake of more clearness, a combined numerical scheme that owes energy-preserving properties is a target to be achieved here. This is done by adapting Galerkin spectral approximation based on Legendre polynomials for Riesz space Laplacian operator side by side to invoke a Cranck–Nickolson scheme in time direction after making order reduction of the original system and a special second-order approximation of the scalar potential derivative. The numerical properties (stability, uniqueness, and convergence) of the scheme are well investigated. Numerical simulations also show that the proposed scheme can inherit the physical properties as the original problem and the numerical solution is stable and convergent to the exact solution.
Energy preserving methods , Galerkin spectral method , Higgs potential , Klein-Gordon equation , Riesz space fractional derivatives
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Department of Mathematics, Faculty of Science, Benha University, Benha, 13511, Egypt
Department of Computational Mathematics and Computer Science, Institute of Natural Sciences and Mathematics, Ural Federal University, 19 Mira St., Yekaterinburg, 620002, Russian Federation
Department of Computer Science, University of Georgia, 7404, Athens, 30602, GA, United States
Department of Mathematics, Nazarbayev University, Nur-Sultan, Kazakhstan
Department of Applied Mathematics, National Research Centre, Cairo, Dokki, 12622, Egypt
Department of Mathematics
Department of Computational Mathematics and Computer Science
Department of Computer Science
Department of Mathematics
Department of Applied Mathematics
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