Keywords : boundary conditions


Some Results in the Theory of Fractional Order Integro-Differential Equation with Boundary Conditions

Azzam S. Younes

AL-Rafidain Journal of Computer Sciences and Mathematics, 2010, Volume 7, Issue 2, Pages 101-114
DOI: 10.33899/csmj.2010.163900

This paper deals with the existence and uniqueness of the solution for a boundary value problem of fractional order integro-differential equation, when  using Banach fixed point theorem and Shafer’s fixed point theorem. This investigation based on the well known Riemann-Liouville fractional differential operator.
 

Flow of Soap Films on Inclined Plane

Joseph G. Abdulahad

AL-Rafidain Journal of Computer Sciences and Mathematics, 2010, Volume 7, Issue 2, Pages 67-78
DOI: 10.33899/csmj.2010.163886

In this paper a mathematical model is constructed to describe a two dimensional flow for an inclined films with an inclination angle  to the horizontal that is drainage under the action of gravity. An asymptotic analysis is employed with the use of lubrication approximation. The film is assumed to be supported by wire frame elements at the ends. We apply the Navier–Stokes equations for flow of an incompressible fluid in two dimensions with specified boundary conditions. We obtain the equations representing the film thickness, the surface concentration, and the surface velocity. We obtain the similarity solutions for extensional flow of the simplified forms of these equations by using Lagrangian coordinate and then we approximate this equation by using Taylor series to obtain another similarity equation that can be used for different values of time.
 

The Existence, Uniqueness And Upper Bounds For Errors Of Six Degree Spline Interpolating The Lacunary Data (0,2,5)

Abbas Y. Al-Bayati; Rostam K. Saeed; Karwan H. Jwamer

AL-Rafidain Journal of Computer Sciences and Mathematics, 2010, Volume 7, Issue 2, Pages 49-57
DOI: 10.33899/csmj.2010.163884

The object of this paper is to obtain the existence, uniqueness and upper bounds for errors of six degree spline interpolating the lacunary data (0,2,5). We also showed that the changes of the boundary conditions and the class of spline functions has a main role in minimizing the upper bounds for error in lacunary interpolation problem. For this reason, in the construction of our spline function which interpolates the lacunary data (0,2,5), we changed the boundary conditions and the class of spline functions which are given by [1] from first derivative to third derivative and the class of spline function from  to .