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Laplace transform for the solution of higher order deformation equations arising in the homotopy analysis method

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Abstract

A new analytic approach for solving nonlinear ordinary differential equations with initial conditions is proposed. First, the homotopy analysis method is used to transform a nonlinear differential equation into a system of linear differential equations; then, the Laplace transform method is applied to solve the resulting linear initial value problems; finally, the solutions to the linear initial value problems are employed to form a convergent series solution to the given problem. The main advantage of the new approach is that it provides an effective way to solve the higher order deformation equations arising in the homotopy analysis method.

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Authors and Affiliations

  1. School of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning, People’s Republic of China, 116024

    Songxin Liang & Junchi Ma

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  1. Songxin Liang
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  2. Junchi Ma
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Correspondence to Songxin Liang.

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The research was partially supported by the National Natural Science Foundation of China (91230103).

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Liang, S., Ma, J. Laplace transform for the solution of higher order deformation equations arising in the homotopy analysis method. Numer Algor 67, 49–57 (2014). https://doi.org/10.1007/s11075-013-9773-0

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  • DOI: https://doi.org/10.1007/s11075-013-9773-0

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