The Study Of Approximate Solution Of A Class Of KdV-Burgers Equation Based On The Homotopy Analysis Method

The homotopy analysis method is an effective way to solve many nonlinearproblems.Compared with the traditional perturbation method，Homotopy analysismethod does not rely on physical parameters, so it applies not only to weaklynonlinear problems, but also applies to the strongly nonlinear problems. Firstly,the paper comprehensive introduces the background and the basic idea of thehomotopy analysis method, and reviewed the relationship between the homotopyanalysis method with the traditional analytical method,then we know Lyaounovartificial small parameter method, expansion method and the Adomiandecomposition method are just the special cases of the homotopy analysis method.Secondly, the paper lists two methods to solve the KdV-Burgers equation,which areBernstein polynomial method and Adomian decomposition method. Finally, thepaper uses the homotopy analysis method to solve a class of KdV-Burgers equationand gets the approximate solution of such equation.Comparing the solutions withthose get from other methods and the exact solution.We get that the homotopyanalysis method is not only simple but also has high accuracy. Therefore thehomotopy analysis method is an effective method for solving nonlinearKdV-Burgers equation.