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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.

Jie Xu, Shusen Xie & Hongfei Fu. (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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