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Volume 21, Issue 2
Two Decoupled and Linearized Block-Centered Finite Difference Methods for the Nonlinear Symmetric Regularized Long Wave Equation

Jie Xu, Shusen Xie & Hongfei Fu

DOI: 10.4208/ijnam2024-1010

Int. J. Numer. Anal. Mod., 21 (2024), pp. 244-267.

Published online: 2024-04

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  • 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.

  • Keywords

Symmetric regularized long wave equation, backward difference formula, Crank-Nicolson, block-centered finite difference method, error estimates.

  • AMS Subject Headings

65H10, 65M06, 65M12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-21-244, author = {Xu , JieXie , Shusen and Fu , Hongfei}, title = {Two Decoupled and Linearized Block-Centered Finite Difference Methods for the Nonlinear Symmetric Regularized Long Wave Equation}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2024}, volume = {21}, number = {2}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/10.4208/ijnam2024-1010}, url = {http://global-sci.org/intro/article_detail/ijnam/23026.html} }
TY - JOUR T1 - Two Decoupled and Linearized Block-Centered Finite Difference Methods for the Nonlinear Symmetric Regularized Long Wave Equation AU - Xu , Jie AU - Xie , Shusen AU - Fu , Hongfei JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 244 EP - 267 PY - 2024 DA - 2024/04 SN - 21 DO - http://doi.org/10.4208/ijnam2024-1010 UR - https://global-sci.org/intro/article_detail/ijnam/23026.html KW - Symmetric regularized long wave equation, backward difference formula, Crank-Nicolson, block-centered finite difference method, error estimates. AB -

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.

Xu , JieXie , Shusen and Fu , Hongfei. (2024). Two Decoupled and Linearized Block-Centered Finite Difference Methods for the Nonlinear Symmetric Regularized Long Wave Equation. International Journal of Numerical Analysis and Modeling. 21 (2). 244-267. doi:10.4208/ijnam2024-1010
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