On the selection of auxiliary functions, operators, and convergence control parameters in the application of the homotopy analysis method to nonlinear differential equations: a general approach.(English)Zbl 1221.65208

Summary: The homotopy analysis method of Liao has been useful in obtaining analytical solutions to various nonlinear differential equations. In this method, one has great freedom to select auxiliary functions, operators, and parameters in order to ensure the convergence of the approximate solutions and to increase both the rate and region of convergence. We discuss in this paper the selection of the initial approximation, auxiliary linear operator, auxiliary function, and convergence control parameter in the application of the homotopy analysis method, in a fairly general setting. Further, we discuss various convergence requirements on solutions.

MSC:

 65L99 Numerical methods for ordinary differential equations
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References:

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