Title

Control of error in the homotopy analysis of semi-linear elliptic boundary value problems

Authors

Authors

R. A. Van Gorder

Comments

Authors: contact us about adding a copy of your work at STARS@ucf.edu

Abbreviated Journal Title

Numer. Algorithms

Keywords

Elliptic boundary value problem; Yamabe equation; Brinkman-Forchheimer; equation; Liouville's equation; Homotopy analysis method; Error analysis; and control; LANE-EMDEN EQUATION; NONLINEAR DIFFERENTIAL-EQUATIONS; VISCOUS-FLOW; PROBLEMS; NON-NEWTONIAN FLUIDS; ANALYTIC SOLUTION; SERIES SOLUTIONS; YAMABE-EQUATION; 2ND KIND; PERTURBATION SOLUTION; FORCED-CONVECTION; Mathematics, Applied

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.

Journal Title

Numerical Algorithms

Volume

61

Issue/Number

4

Publication Date

1-1-2012

Document Type

Article

Language

English

First Page

613

Last Page

629

WOS Identifier

WOS:000310999600005

ISSN

1017-1398

Share

COinS