Transformation of the second order boundary value problem into integral form : different approaches and a numerical solution

• Autorzy: Siedlecki J. , Ciesielski M. , Błaszczyk T.

Identyfikatory

DOI

10.17512/jamcm.2015.3.11

• Języki publikacji: EN

Abstrakty

EN

In this paper we present different approaches to the transformation of the second order ordinary differential equation, with respect to adequate boundary conditions, into integral equations. The obtained equations are Fredholm integral equations of the second kind. Next, a numerical method based on quadrature methods has been proposed to get an approximate solution of these equations.

Słowa kluczowe

EN

BVP problem; Fredholm integral equation; Fubini's theorem; numerical methods

PL

zagadnienie wartości brzegowych; równanie całkowe Fredholma; twierdzenie Fubinisa; metody numeryczne

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2015
• Tom: Vol. 14, nr 3
• Strony: 103--108
• Opis fizyczny: Bibliogr. 7 poz., rys.

Twórcy

autor

Siedlecki J.

• Institute of Mathematics, Czestochowa University of Technology Częstochowa, Poland

autor

Ciesielski M.

• Institute of Computer and Information Sciences Czestochowa University of Technology, Czestochowa, Poland

autor

Błaszczyk T.

• Institute of Mathematics, Czestochowa University of Technology Częstochowa, Poland

Bibliografia

• [1] Agarwal R.P., O'Regan D., An Introduction to Ordinary Differential Equations, Springer, New York 2008.
• [2] Kukla S., Funkcje Greena i ich zastosowania, Wyd. Politechniki Częstochowskiej, Częstochowa 2009.
• [3] Zaitsev V.F., Polyanin A.D., Handbook of Exact Solutions for Ordinary Differential Equations, CRC Press, New York 1995.
• [4] Collins P.J., Differential and Integral Equations, Oxford University Press, New York 2006.
• [5] Polyanin A.D., Manzhirov A.V., Handbook of Integral Equations (Second Edition), Taylor & Francis Group, Boca Raton 2008.
• [6] Press W.H., Teukolsky S.A., Vetterling W.T., Flannery B.P., Numerical Recipes: The Art of Scientific Computing (3rd ed.), Cambridge University Press, New York 2007.
• [7] Atkinson K.E., The Numerical Solution of Integral Equations of the Second Kind, Cambridge University Press, 2009.