This paper is dealing with non-polynomial spline functions "generalized spline" to find the approximate solution of linear Volterra integro-differential equations of the second kind and extension of this work to solve system of linear Volterra integro-differential equations. The performance of generalized spline functions are illustrated in test examples

A particular solution of the two and three dimensional unsteady state thermal or mass diffusion equation is obtained by introducing a combination of variables of the form,
η = (x+y) / √ct , and η = (x+y+z) / √ct, for two and three dimensional equations
respectively. And the corresponding solutions are,
θ (t,x,y) = θ₀ erfc (x+y)/√8ct and θ( t,x,y,z) =θ₀ erfc (x+y+z/√12ct)

The aim of this paper is to propose a reliable iterative method for resolving many types of Volterra - Fredholm Integro - Differential Equations of the second kind with initial conditions. The series solutions of the problems under consideration are obtained by means of the iterative method. Four various problems are resolved with high accuracy to make evident the enforcement of the iterative method on such type of integro differential equations. Results were compared with the exact solution which exhibits that this technique was compatible with the right solutions, simple, effective and easy for solving such problems. To evaluate the results in an iterative process the MATLAB is used as a math program for the calculations.

Common walnut (Juglans regia L.) has a long cultivation history, given its highly valuable wood and rich nutritious nuts. The Iranian Plateau has been considered as one of the last glaciation refugia and a centre of origin and domestication for the common walnut. However, a prerequisite to conserve or utilize the genetic resources of J. regia in the plateau is a comprehensive evaluation of the genetic diversity that is conspicuously lacking. In this regard, we used 31 polymorphic simple sequence repeat (SSR) markers to delineate the genetic variation and population stru

KE Sharquie, AA Noaimi, AA Zeena, IOSR J Dent Med Sci, 2015 - Cited by 5