A Conservative Linear High-order Compact Finite Difference Scheme for the Two-dimensional Regularized Long Wave Equation

This paper proposes a high-order numerical scheme for solving the two-dimensional nonlinear regularized long wave (RLW) equation, which is linear, conservative, and stable. The temporal derivative is discretized using the Crank-Nicolson scheme, while the spatial first-order and second-order derivatives are approximated using the fourth-order Padé scheme and the fourth-order compact finite difference scheme, respectively, achieving second-order temporal accuracy and fourth-order spatial accuracy. The nonlinear term is linearized through the Taylor series expansion method. Furthermore, theoretical analysis is conducted to prove the properties of the scheme, including conservation, unconditional stability, and the existence and uniqueness of the numerical solution. Extensive numerical experiments thoroughly validate the reliability, conservation properties, stability, and computational efficiency of the proposed scheme. The results demonstrate that the accuracy of this method surpasses other existing schemes documented in the literature. Mathematics Subject Classi cation. 35Q75; 65M06; 65M12: