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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 982810, 7 pages
http://dx.doi.org/10.1155/2013/982810
Research Article

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

Hebei University of Engineering, Handan 056038, China

Received 17 March 2013; Accepted 14 June 2013

Academic Editor: Evangelos J. Sapountzakis

Copyright © 2013 Xing Ruyi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.