Methods for the Control of Convergence in Obtained Solutions

Kuppalapalle Vajravelu () and Robert A. van Gorder ()
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Kuppalapalle Vajravelu: University of Central Florida, Department of Mathematics
Robert A. van Gorder: University of Central Florida, Department of Mathematics

Chapter Chapter 3 in Nonlinear Flow Phenomena and Homotopy Analysis, 2012, pp 53-75 from Springer

Abstract: Abstract The homotopy analysis method of Liao has proven useful in obtaining analytical solutions to various nonlinear differential equations. As discussed in the preceding chapter, 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. In the present chapter, we discuss 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.

Keywords: Series Solution; Nonlinear Differential Equation; Homotopy Analysis Method; Homotopy Perturbation Method; Auxiliary Linear Operator (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-32102-3_3

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DOI: 10.1007/978-3-642-32102-3_3

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