A computational method based on Hermite wavelets for two‐dimensional Sobolev and regularized long wave equations in fluids

Abstract

This paper deals with the numerical solutions of two‐dimensional Sobolev and regularized long wave equations which commonly emerge in the flow of fluids or used to explain motion of wave in media. The proposed computational method in this paper is based on Hermite wavelets. We first discretize time derivatives in the considered equations by finite difference approaches then we use Hermite wavelets for discretization of space variables. By doing so computing the numerical solutions of Sobolev and regularized long wave equations is reduced to computing the solution of an algebraic system of equations whose solution gives Hermite wavelet coefficients. Then with these wavelet coefficients numerical solutions can be computed successively. The main objective of this paper is to indicate that Hermite wavelets based computational method is proper and efficient for two‐dimensional Sobolev and regularized long wave equations. We consider five test problems and calculate L2 and L∞ error norms for comparison of results of the current paper with the exact results and with the results of earlier studies based on such as finite difference, finite element and meshless methods. The obtained results verify the feasibility and efficiency of the proposed method.