Two Decoupled and Linearized Block-Centered Finite Difference Methods for the Nonlinear Symmetric Regularized Long Wave Equation
Year: 2024
Author: Jie Xu, Shusen Xie, Hongfei Fu
International Journal of Numerical Analysis and Modeling, Vol. 21 (2024), Iss. 2 : pp. 244–267
Abstract
In this paper, by introducing a new flux variable, two decoupled and linearized block-centered finite difference methods are developed and analyzed for the nonlinear symmetric regularized long wave equation, where the two-step backward difference formula and Crank-Nicolson temporal discretization combined with linear extrapolation technique are employed. Under a reasonable time stepsize ratio restriction, i.e., $∆t=o(h^{1/4}),$ second-order convergence for both the primal variable and its flux are rigorously proved on general non-uniform spatial grids. Moreover, based upon the convergence results and inverse estimate, stability of two methods are also demonstrated. Ample numerical experiments are presented to confirm the theoretical analysis.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ijnam2024-1010
International Journal of Numerical Analysis and Modeling, Vol. 21 (2024), Iss. 2 : pp. 244–267
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Symmetric regularized long wave equation backward difference formula Crank-Nicolson block-centered finite difference method error estimates.