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A new application of the homotopy analysis method: solving the Sturm-Liouville problems. (English) Zbl 1221.65189
Summary: 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. We observe that the auxiliary parameter $\hbar$, 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.

65L99Numerical methods for ODE
Full Text: DOI
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