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

Authors:
Songxin Liang;David J. Jeffrey
Affiliations:
Department of Applied Mathematics, University of Western Ontario, London, Canada N6A 5B7;Department of Applied Mathematics, University of Western Ontario, London, Canada N6A 5B7
Venue:
Numerical Algorithms
Year:
2011

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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.