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Article
Publication date: 4 May 2010

Feyed Ben Zitoun and Yves Cherruault

The purpose of this paper is to present a method for solving nonlinear differential equations with constant and/or variable coefficients and with initial and/or boundary…

792

Abstract

Purpose

The purpose of this paper is to present a method for solving nonlinear differential equations with constant and/or variable coefficients and with initial and/or boundary conditions.

Design/methodology/approach

The method converts the nonlinear boundary value problem into a system of nonlinear algebraic equations. By solving this system, the solution is determined. Comparing the methodology with some known techniques shows that the present approach is simple, easy to use, and highly accurate.

Findings

The proposed technique allows us to obtain an approximate solution in a series form. Test problems are given to illustrate the pertinent features of the method. The accuracy of the numerical results indicates that the technique is efficient and well suited for solving nonlinear differential equations.

Originality/value

The present approach provides a reliable technique, which avoids the tedious work needed by classical techniques and existing numerical methods. The nonlinear problem is solved without linearizing or discretizing the nonlinear terms of the equation. The method does not require physically unrealistic assumptions, linearization, discretization, perturbation, or any transformation in order to find the solutions of the given problems.

Details

Kybernetes, vol. 39 no. 4
Type: Research Article
ISSN: 0368-492X

Keywords

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Article
Publication date: 2 March 2012

Feyed Ben Zitoun and Yves Cherruault

The purpose of this paper is to present a method for solving nonlinear integro‐differential equations with constant/variable coefficients and with initial/boundary conditions.

360

Abstract

Purpose

The purpose of this paper is to present a method for solving nonlinear integro‐differential equations with constant/variable coefficients and with initial/boundary conditions.

Design/methodology/approach

The method converts the given problem into a system of nonlinear algebraic equations. By solving this system, the solution is determined. Comparing the methodology with some known techniques shows that the present approach is simple, easy to use and highly accurate.

Findings

The proposed technique allows an approximate solution in a series form to be obtained. Test problems are solved to illustrate the pertinent features of the method. The accuracy of the numerical results indicates that the technique is efficient and well suited for solving nonlinear integro‐differential equations.

Originality/value

The present approach provides a reliable technique which avoids the tedious work needed by the classical techniques.

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Article
Publication date: 12 June 2009

Feyed Ben Zitoun and Yves Cherruault

The purpose of this paper is to present a method for solving nonlinear integral equations of the second and third kind.

276

Abstract

Purpose

The purpose of this paper is to present a method for solving nonlinear integral equations of the second and third kind.

Design/methodology/approach

The method converts the nonlinear integral equation into a system of nonlinear equations. By solving the system, the solution can be determined. Comparing the methodology with some known techniques shows that the present approach is simple, easy to use, and highly accurate.

Findings

The proposed technique allows the authors to obtain an approximate solution in a series form. Test problems are given to illustrate the pertinent features of the method. The accuracy of the numerical results indicates that the technique is efficient and well‐suited for solving nonlinear integral equations.

Originality/value

The present approach provides a reliable technique that avoids the difficulties and massive computational work if compared with the traditional techniques and does not require discretization in order to find solutions to the given problems.

Details

Kybernetes, vol. 38 no. 5
Type: Research Article
ISSN: 0368-492X

Keywords

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Article
Publication date: 12 June 2009

Feyed Ben Zitoun and Yves Cherruault

The purpose of this paper is to present a new algorithm for solving nonlinear boundary value problems (BVPs).

267

Abstract

Purpose

The purpose of this paper is to present a new algorithm for solving nonlinear boundary value problems (BVPs).

Design/methodology/approach

The method converts the nonlinear BVP into a system of nonlinear equations. By solving the system, the solution can be determined. Comparing the methodology with some known techniques shows that the present approach is simple, easy to use and highly accurate.

Findings

The proposed technique allows us to obtain an approximate solution in a series form which satisfies all the given conditions. Test problems are given to illustrate the pertinent features of the method. The accuracy of the numerical results indicates that the technique is efficient and well suited for solving nonlinear differential equations with initial and boundary conditions.

Originality/value

The paper provides a reliable technique which avoids the tedious work needed by classical techniques and existing numerical methods and does not require discretization in order to find the solutions of the given problems.

Details

Kybernetes, vol. 38 no. 5
Type: Research Article
ISSN: 0368-492X

Keywords

Available. Content available
Article
Publication date: 12 June 2009

Yves Cherruault

905

Abstract

Details

Kybernetes, vol. 38 no. 5
Type: Research Article
ISSN: 0368-492X

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