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Generalized homotopy method for solving nonlinear differential equations

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Abstract

In this paper, a new tool for the solution of nonlinear differential equations is presented. The generalized homotopy method (GHM) provides highly accurate approximations of the differential equation using a few linear algebraic terms. In order to assess the benefits of this proposal, two nonlinear problems are solved and compared against other semi-analytic or numerical methods. The obtained results show that GHM is a powerful tool capable to generate highly accurate solutions.

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Acknowledgments

We gratefully acknowledge the financial support from the National Council for Science and Technology of Mexico (CONACyT) through Grant CB-2010-01 #157024. The author wants to express his gratitude to Roberto Castaneda-Sheissa, Rogelio-Alejandro Callejas-Molina, and Roberto Ruiz-Gomez for their contribution to this project.

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  1. Electronic Instrumentation and Atmospheric Sciences School, University of Veracruz, Cto. Gonzalo Aguirre Beltrán S/N, 91000 , Xalapa, VER, México

    Hector Vazquez-Leal

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  1. Hector Vazquez-Leal
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Correspondence to Hector Vazquez-Leal.

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Communicated by Cristina Turner.

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Vazquez-Leal, H. Generalized homotopy method for solving nonlinear differential equations. Comp. Appl. Math. 33, 275–288 (2014). https://doi.org/10.1007/s40314-013-0060-4

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