Abstract
Volterra – Fredholm integral equations (VFIEs) have a massive interest from researchers recently. The current study suggests a collocation method for the mixed Volterra - Fredholm integral equations (MVFIEs)."A point interpolation collocation method is considered by combining the radial and polynomial basis functions using collocation points". The main purpose of the radial and polynomial basis functions is to overcome the singularity that could associate with the collocation methods. The obtained interpolation function passes through all Scattered Point in a domain and therefore, the Delta function property is the shape of the functions. The exact solution of selective solutions was compared with the results obtained from the numerical experiments in order to investigate the accuracy and the efficiency of scheme.
Highlights
Consider the general mixed Volterra - Fredholm integral equation has the from u(s, t) = f(s, t) + ∫0t ∫Ω K(s, t, x, y, u(x, y))dxdy (s, t) ∈ I = Ω × [o, T] (1)where u(s, t) is unknown function should to be found, f(s, t) and K(s, t, x, y, u(x, y)) are given analytic functions on I = Ω × [o, T] and C(I2 ×R),respectively and Ω is close subset on R, with norm ||.|| .Equations of this type arise in the main branches of modern mathematics that appear in various applied areas including mechanics, physics and engineering...etc
In this work, we have studied a collocation method to solve linear and non-linear mixed Volterra – Fredholm integral equations (MVFIEs)
Zeros of shifts Legendre are used as collocation points
Summary
The aim of this paper is to apply collocation method for solving mixed Volterra – Fredholm integral equations (MVFIEs) which have the formula (Eq.[1]). Constructs the approximation function u(s, t) to access the node points'(8). Where di is the distance between the node (si, ti) and the interpolating point(s, t) in the Euclidean 2. - dimensional space di could be described as di = [(s − si)2 + (t − ti)2]2 The terms of polynomial basis function are as following: ɃT = (PIM) approximating function (Eq.13) is firstly obtained from a set of points. It calculated in a straight forward by differentiating such a closed form (RBF).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
