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A semi‐numerical technique for solving the multi‐point boundary value problems and engineering applications

Mehdi Dehghan (Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran)
Fatemeh Shakeri (Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 20 September 2011

Abstract

Purpose

Multi‐point boundary value problems have important roles in the modelling of various problems in physics and engineering. This paper aims to present the solution of ordinary differential equations with multi‐point boundary value conditions by means of a semi‐numerical approach which is based on the homotopy analysis method.

Design/methodology/approach

The convergence of the obtained solution is expressed and some typical examples are employed to illustrate validity, effectiveness and flexibility of this procedure. This approach, in contrast to perturbation techniques, is valid even for systems without any small/large parameters and therefore it can be applied more widely than perturbation techniques, especially when there do not exist any small/large quantities.

Findings

Unlike other analytic techniques, this approach provides a convenient way to adjust and control the convergence of approximation series. Some applications will be briefly introduced.

Originality/value

The paper shows how an important boundary value problem is solved with a semi‐analytical method.

Keywords

Citation

Dehghan, M. and Shakeri, F. (2011), "A semi‐numerical technique for solving the multi‐point boundary value problems and engineering applications", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 21 No. 7, pp. 794-809. https://doi.org/10.1108/09615531111162783

Publisher

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Emerald Group Publishing Limited

Copyright © 2011, Emerald Group Publishing Limited