In this paper we use non-polynomial spline functions to develop numerical methods to approximate the solution of 2nd kind Volterra integral equations. Numerical examples are presented to illustrate the applications of these method, and to compare the computed results with other known methods.

In this paper, Touchard polynomials (TPs) are presented for solving Linear Volterra integral equations of the second kind (LVIEs-2k) and the first kind (LVIEs-1k) besides, the singular kernel type of this equation. Illustrative examples show the efficiency of the presented method, and the approximate numerical (AN) solutions are compared with one another method in some examples. All calculations and graphs are performed by program MATLAB2018b.

The main work of this paper is devoted to a new technique of constructing approximated solutions for linear delay differential equations using the basis functions power series functions with the aid of Weighted residual methods (collocations method, Galerkin’s method and least square method).

هناك دائما حاجة إلى طريقة فعالة لتوليد حل عددي أكثر دقة للمعادلات التكاملية ذات النواة المفردة أو المفردة الضعيفة لأن الطرق العددية لها محدودة. في هذه الدراسة ، تم حل المعادلات التكاملية ذات النواة المفردة أو المفردة الضعيفة باستخدام طريقة متعددة حدود برنولي. الهدف الرئيسي من هذه الدراسة هو ايجاد حل تقريبي لمثل هذه المشاكل في شكل متعددة الحدود في سلسلة من الخطوات المباشرة. أيضا ، تم افتراض أن مقام النواة

In this paper a modified approach have been used to find the approximate solution of ordinary delay differential equations with constant delay using the collocation method based on Bernstien polynomials.

In this paper, a new analytical method is introduced to find the general solution of linear partial differential equations. In this method, each Laplace transform (LT) and Sumudu transform (ST) is used independently along with canonical coordinates. The strength of this method is that it is easy to implement and does not require initial conditions.

The research aims to find approximate solutions for two dimensions Fredholm linear integral equation. Using the two-variables of the Bernstein polynomials we find a solution to the approximate linear integral equation of the type two dimensions. Two examples have been discussed in detail.

The major aim of this work is to propose a novel method, the Variation Iteration Adomain Decomposition Method (VIADM), an iterative semi-analytical method to achieve an approximate analytical solution for nonlinear (Volterra / Fredholm) integral equations. This technique depends on applying the Adomain Decomposition Method (ADM) to a nonlinear term that can be solved using Adomain polynomials. The VIADM has been used to break down the Volterra integral equation solution into infinite components. Furthermore, some illustrative examples are given, and the results obtained indicate the proposed method’s accuracy, efficiency, and reliability.

The non static chain is always the problem of static analysis so that explained some of theoretical work, the properties of statistical regression analysis to lose when using strings in statistic and gives the slope of an imaginary relation under consideration.  chain is not static can become static by adding variable time to the multivariate analysis the factors to remove the general trend as well as variable placebo seasons to remove the effect of seasonal .convert the data to form exponential or logarithmic , in addition to using the difference repeated d is said in this case it integrated class d. Where the research contained in the theoretical side in parts in the first part the research methodology ha