Title

Control Of Error In The Homotopy Analysis Of Semi-Linear Elliptic Boundary Value Problems

Keywords

Brinkman-Forchheimer equation; Elliptic boundary value problem; Error analysis and control; Homotopy analysis method; Liouville's equation; Yamabe equation

Abstract

In the present paper, we have considered three methods with which to control the error in the homotopy analysis of elliptic differential equations and related boundary value problems, namely, control of residual errors, minimization of error functionals, and optimal homotopy selection through appropriate choice of auxiliary function H(x). After outlining the methods in general, we consider three applications. First, we apply the method of minimized residual error in order to determine optimal values of the convergence control parameter to obtain solutions exhibiting central symmetry for the Yamabe equation in three or more spatial dimensions. Secondly, we apply the method of minimizing error functionals in order to obtain optimal values of the convergnce control parameter for the homotopy analysis solutions to the Brinkman-Forchheimer equation. Finally, we carefully selected the auxiliary function H(x) in order to obtain an optimal homotopy solution for Liouville's equation. © 2012 Springer Science+Business Media, LLC.

Publication Date

12-1-2012

Publication Title

Numerical Algorithms

Volume

61

Issue

4

Number of Pages

613-629

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/s11075-012-9554-1

Socpus ID

84869218514 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84869218514

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