Li, H, Kang, L, Li, M, Luo, X and Xiang, S (2024) Hamiltonian conserved Crank-Nicolson schemes for a semi-linear wave equation based on the exponential scalar auxiliary variables approach. Electronic Research Archive (ERA), 32 (7). pp. 4433-4453.

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Abstract

The keys to constructing numerical schemes for nonlinear partial differential equations are accuracy, handling of the nonlinear terms, and physical properties (energy dissipation or conservation). In this paper, we employ the exponential scalar auxiliary variable (E-SAV) method to solve a semi-linear wave equation. By defining two different variables and combining the Crank−Nicolson scheme, two semi-discrete schemes are proposed, both of which are second-order and maintain Hamiltonian conservation. Two numerical experiments are presented to verify the reliability of the theory.

Item Type:	Article
Uncontrolled Keywords:	Crank-Nicolson scheme; error analysis; exponential scalar auxiliary variable; semi-linear wave equation; semi-linear wave equation; exponential scalar auxiliary variable; error analysis; Crank-Nicolson scheme
Subjects:	T Technology > TA Engineering (General). Civil engineering (General)
Divisions:	Engineering
Publisher:	American Institute of Mathematical Sciences (AIMS)
SWORD Depositor:	A Symplectic
Date Deposited:	10 Oct 2024 10:18
Last Modified:	10 Oct 2024 10:30
DOI or ID number:	10.3934/era.2024200
URI:	https://researchonline.ljmu.ac.uk/id/eprint/24489

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