Finding Discontinuous Solutions to the Differential-Difference Equations by the Homotopy Analysis Method

• 来源期刊: 中国物理快报（英文版）
• 年，卷（期）: 2013,（2）
• 页码范围: 11-15
• 页数: 5页
• 语种: 英文
• DOI: 10.1088/0256-307X/30/2/020204

摘要

It is difficult to solve nonlinear problems by analytical techniques,especially for the nonlinear differential-difference equations.Currently,finding the explicit analytic solutions of the nonlinear differential equations is extremely important in mathematical physics.In recent years,an analytical method for strongly nonlinear problems,namely the homotopy analysis method (HAM),[1,2] has been developed.Liao[1,2] employed the basic ideas of the homotopy in topology to propose the method for nonlinear problems.[3-8] This method has been successfully applied to solving many types of nonlinear problems such as the nonlinear model of diffusion and reaction in porous catalysts,[9] nonlinear waves,[10] the magnetohydrodynamic flows of non-Newtonian fluids viscous flow past a porous plate,[11] the flows of an Oldroyd 6-constant fluid,[12] nano boundary layer flows,[13] micropolar fluids,[14] the soliton wave with one-loop,[15]the shallow water solitary wave problem,[16] and so on.All the applications of the HAM are restricted to the integral-differential equation.In 2007,Wang and Zou extended the homotopy analysis method to solve the differential-difference equation and proposed the differential-difference equations-homotopy analysis method (DDE-HAM).