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An analytical approach for solving nonlinear boundary value problems in finite domains

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Abstract

Based on the homotopy analysis method (HAM), a general analytical approach for obtaining approximate series solutions to nonlinear two-point boundary value problems in finite domains is proposed. To demonstrate its effectiveness, this approach is applied to solve three nonlinear problems, and the analytical solutions obtained are more accurate than the numerical solutions obtained via the shooting method and the sinc-Galerkin method.

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Authors and Affiliations

  1. Department of Applied Mathematics, University of Western Ontario, London, ON, Canada, N6A 5B7

    Songxin Liang & David J. Jeffrey

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  1. Songxin Liang
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  2. David J. Jeffrey
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Correspondence to Songxin Liang.

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Liang, S., Jeffrey, D.J. An analytical approach for solving nonlinear boundary value problems in finite domains. Numer Algor 56, 93–106 (2011). https://doi.org/10.1007/s11075-010-9375-z

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  • DOI: https://doi.org/10.1007/s11075-010-9375-z

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