Algorithms using the second order of B -splines [B (x)] and the third order of B -splines [B,3(x)] are derived to solve 1' , 2nd and 3rd linear Fredholm integro-differential equations (F1DEs). These new procedures have all the useful properties of B -spline function and can be used comparatively greater computational ease and efficiency.The results of these algorithms are compared with the cubic spline function.Two numerical examples are given for conciliated the results of this method.

in this paper the collocation method will be solve ordinary differential equations of retarted arguments also some examples are presented in order to illustrate this approach

In this paper Heun method has been used to find numerical solution for first order nonlinear functional differential equation. Moreover, this method has been modified in order to treat system of nonlinear functional differential equations .two numerical examples are given for conciliated the results of this method.

The propagation of laser beam in the underdense deuterium plasma has been studied via computer simulation using the fluid model. An appropriate computer code “HEATER” has been modified and is used for this purpose. The propagation is taken to be in a cylindrical symmetric medium. Different laser wavelengths (1 = 10.6 m, 2 = 1.06 m, and 3 = 0.53 m) with a Gaussian pulse type and 15 ns pulse widths have been considered. Absorption energy and laser flux have been calculated for different plasma and laser parameters. The absorbed laser energy showed maximum for  = 0.53 m. This high absorbitivity was inferred to the effect of the pondermotive force.

In this paper, the construction of Hermite wavelets functions and their operational matrix of integration is presented. The Hermite wavelets method is applied to solve nth order Volterra integro diferential equations (VIDE) by expanding the unknown functions, as series in terms of Hermite wavelets with unknown coefficients. Finally, two examples are given

The nonlinear optical properties for polymeric (PMMA) doping with dye Rhodmine (R3Go) has been studied .The samples are prepared by normal polymerization method with concentrations of 5x10^-5mol/l and a thickness of 272.5µm.

                         Plasma effect was studied on samples prepared before and after exposure to the Nd: YAG laser for three times 5, 10 and 15 minutes. Z-Scan technique is used to determine the nonlinear optical properties such as; refractive index (n₂) and the coefficient of nonlinear absorption (β). It was found that the nonlinear properties is change by increasi