期刊
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
卷 16, 期 1, 页码 112-126出版社
ELSEVIER
DOI: 10.1016/j.cnsns.2010.04.004
关键词
Homotopy analysis method; Multiple solutions; Two point Sturm-Liouville problems; Four point Sturm-Liouville problems
In this paper, the homotopy analysis method (HAM) is applied to numerically approximate the eigenvalues of the second and fourth-order Sturm-Liouville problems. These eigenvalues are calculated by starting the HAM algorithm with one initial guess. In this paper, it can be observed that the auxiliary parameter h, which controls the convergence of the HAM approximate series solutions, also can be used in predicting and calculating multiple solutions. This is a basic and more important qualitative difference in analysis between HAM and other methods. (C) 2010 Elsevier B.V. All rights reserved.
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