Application Of Homotopy Perturbation Method To Solve Nonlinear Equations

The nonlinear evolution equations which arise in mathematical physics and engineering technology are used to approximately describe the natural law.Thus it is important to find the approximate solutions of the nonlinear equation.Resent years,many numerical methods for soving the nonlinear evolution equations are proposed.such as, difference method, spectral method,method of lines,homotopy perturbation method and so on.In this paper,the applications of the method of lines and the homotopy perturbation method for solving nonlinear evolution equations are mainly studied and KdV equation, Burgers equation, KdV-Burgers equation, variable-coefficients KdV equation,variable- coefficients Burgers equation are solved by the methodof lines. KdV equation, Burgers equation,KdV-Burgers equation, BBM equation, (2+1)-dimensional breaking soliton equation, (3+1)-dimensional KP equation, variable-coefficients KdV equation, variable-coefficients Burgers equation, (2+1)-dimensionalvariable-coefficients breaking soliton equation, (3+1)- dimensional variable-coefficients ZK equation are solved bythe homotopy perturbation method.The results shows that the homotopy perturbation method has the advantages of high accuracy and less amount of calculation compared to other numerical methods.