A Novel Wavelet-Homotopy Galerkin Method for Unsteady Nonlinear Wave Equations
作者机构：State Key Lab of Ocean EngineeringSchool of Naval ArchitectureOcean and Civil EngineeringShanghai Jiao Tong UniversityShanghai 200240China
出 版 物：《Advances in Applied Mathematics and Mechanics》 (应用数学与力学进展（英文）)
年 卷 期：2023年第15卷第4期
页 面：964-983页
核心收录：
学科分类：07[理学] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）]
主 题：Coiflet wavelet homotopy analysis method wavelet-homotopy method wave equations unsteady
摘 要：The Coiflet wavelet-homotopy Galerkin method is extended to solve unsteady nonlinear wave equations for the first time.The Korteweg-de Vries(KdV)equation,the Burgers equation and the Korteweg-de Vries-Burgers(KdVB)equation are examined as illustrative examples.Validity and accuracy of the proposed method are assessed in terms of relative variance and the maximum error norm.Our results are found in good agreement with exact solutions and numerical solutions reported in previous studies.Furthermore,it is found that the solution accuracy is closely related to the resolution level and the convergence-control parameter.It is also found that our proposed method is superior to the traditional homotopy analysis method when dealing with unsteady nonlinear problems.It is expected that this approach can be further used to solve complicated unsteady problems in the fields of science and engineering.
维普期刊数据库