Crank-Nicolson/finite element approximation for the Schrödinger equation in the de Sitter spacetime
Selvitopi H. Zaky M.A. Hendy A.S.
2021IOP Publishing Ltd
Physica Scripta
2021#96Issue 12
Central to much of science, engineering, and society today is the building of mathematical models to represent complex processes. Recently, the non-relativistic limit of nonlinear Klein-Gordon equations in de Sitter spacetime has been used to derive Schrödinger equations with weighted nonlinear terms In this paper, numerical simulations are constructed to clarify the behavior of the solution in both one- and two-dimensions. These simulations are constructed based on the Crank-Nicolson scheme in the time direction and the Galerkin finite element in the spatial direction. The nonlinear system of algebraic equations resulting from the constructed scheme is solved using Newton’s method. It is also demonstrated that the numerical approximation converges to the exact one.
Convergence analysis , Crank-Nicolson scheme , De Sitter spacetime , Galerkin finite element , Schrödinger equation
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Department of Mathematics, Faculty of Sciences, Erzurum Technical University, Erzurum, 25050, Turkey
Department of Applied Mathematics, Physics Division, National Research Centre, Dokki, Cairo, 12622, Egypt
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
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 Mathematics, Faculty of Science, Benha University, Benha, 13511, Egypt
Department of Mathematics
Department of Applied Mathematics
Institute of Mathematics and Mathematical Modeling
Department of Computational Mathematics and Computer Science
Department of Mathematics
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