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

Siedlecki J., Ciesielski M., Błaszczyk T.

Journal of Applied Mathematics and Computational Mechanics

2015

Vol. 14, nr 3

103--108

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.

New inequalities of Cebysev type for double integrals

Pachpatte B.

Demonstratio Mathematica

2007

Vol. 40, nr 1

43-50

In this paper, we establish new inequalities of Čebyšev type involving functions of two independent variables by using certain integral identities.