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 - <p style="text-align: justify;">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.</p>