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Methods for the Control of Convergence in Obtained Solutions

  • Kuppalapalle Vajravelu
  • Robert A. van Gorder

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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Kuppalapalle Vajravelu
    • 1
  • Robert A. van Gorder
    • 1
  1. 1.Department of MathematicsUniversity of Central FloridaOrlandoUSA

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