Wavelet-Based Homotopy Analysis Method for Nonlinear Matrix System and Its Application in Burgers Equation

Abstract

To generalize the homotopy analysis method (HAM) to multidegree-of-freedom nonlinear system, the adaptive precise integration method (APIM) is introduced into the HAM, with which the almost exact value of the exponential matrix can be obtained. Combining the interval interpolation wavelet collocation method, HAM-based APIM can be employed to solve the nonlinear PDEs. As an example, Burgers equation is spatially discretized by the interval quasi-Shannon wavelet collocation method and solved by the proposed method to illustrate the effectiveness and great potential of the homotopy analysis method in nonlinear problems.