Boundary integral solution for a class of fourth-order two-point boundary value problems

• Autorzy: Al-Gahtani H. J.

Identyfikatory

DOI

10.17512/jamcm.2016.3.01

• Języki publikacji: EN

Abstrakty

EN

In this paper, a boundary integral method is proposed for the solution of a class of fourth-order two-boundary value problems described by the equation y^iv+P(x, y, y^’, y^’’, y^’’’) = 0, x ∈ ( 0,L), where P is a polynomial function of its arguments. The differential equation is cast in an integral form and the weighted residual technique is used to generate the corresponding boundary integral equations. The boundary integral equations are then, solved by expressing the dependent variable, y, in terms of a power series. The proposed method is tested through four examples to show the applicability of the method to solve a wide range of fourth-order differential equations including the nonlinear ones.

Słowa kluczowe

EN

boundary integral method; fourth-order differential equation; nonlinear ordinary differential equations

PL

nieliniowe równania różniczkowe zwyczajne; równanie różniczkowe czwartego rzędu

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2016
• Tom: Vol. 15, nr 3
• Strony: 5--13
• Opis fizyczny: Bibliogr. 10 poz., tab.

Twórcy

autor

Al-Gahtani H. J.

• King Fahd University of Petroleum & Minerals Dhahran, Saudi Arabia

Bibliografia

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• [2] Butcher J., The Numerical Analysis of Ordinary Differential Equations: Runge-Kutta and General Linear Methods, John Wiley, 1987.
• [3] Butcher J., The Numerical Methods for Ordinary Differential Equations: Runge-Kutta and General Linear Methods, John Wiley, 2003.
• [4] LeVeque R., Finite difference methods for ordinary and partial differential equations, SIAM, 2007.
• [5] Banerjee P., Butterheld R., Boundary Element Methods in Engineering Science, McGraw-Hill, London 1981.
• [6] Butterfield R., New concepts illustrated by old problems, In: P.K. Banerjee, R. Butterfield (ed.), Development in Boundary Element Methods, London 1982.
• [7] Al-Gahtani H., Integral-based solution for a class of second order boundary value problems, Applied Mathematics and Computation 1999, 98, 43-48.
• [8] Ma T., Silva J., Iterative solutions for a beam equation with nonlinear boundary conditions of third order, Applied Mathematics and Computation 2004, 159, 11-18.
• [9] Geng F., Iterative reproducing kernel method for a beam equation with third-order nonlinear boundary conditions. Mathematical Sciences 2012, 6-1, 1-4.
• [10] El-Gamel M., Behiry S., Hashish H., Numerical method for the solution of special nonlinear fourth-order boundary value problems, Applied Mathematics and Computation 2004, 159, 11-18.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.