NEW ALGORITHMS FOR NUMERICAL SOLUTION OF NONLINEAR INTEGRO-DIFFERENTIAL EQUATIONS OF THIRD ORDER USING HAAR WAVELETS M. Fayyaz a and M. Azram b * Department of Computer Science, CECOS University Peshawar, Pakistan. [email protected] b Faculty of Engineering, IIUM, Kuala Lumpur 50728, Malaysia. [email protected] ABSTRACT: This paper deals with the extension of earlier work [3] (designed for Fre...

Integral and integro-differential equations are one of the most useful mathematical tools in both pure and applied mathematics. In this article, we present a variational iteration method for solving Fredholm integro-differential equations. This study provides an analytical approximation to determine the behavior of the solution. To show the efficiency of the present method for our proble...

this paper presents a computational method for solving two types of integro-differential equations, system of nonlinear high order volterra-fredholm integro-differential equation(vfides) and nonlinear fractional order integro-differential equations. our tools for this aims is operational matrices of integration and fractional integration. by this method the given problems reduce to solve a syst...

the spline collocation method  is employed to solve a system of linear and nonlinear fredholm and volterra integro-differential equations. the solutions are collocated by cubic b-spline and the integrand is approximated by the newton-cotes formula. we obtain the unique solution for linear and nonlinear system $(nn+3n)times(nn+3n)$ of integro-differential equations. this approximation reduces th...

in this letter, the numerical scheme of nonlinear volterra-fredholm integro-differential equations is proposed in a reproducing kernel hilbert space (rkhs). the method is constructed based on the reproducing kernel properties in which the initial condition of the problem is satised. the nonlinear terms are replaced by its taylor series. in this technique, the nonlinear volterra-fredholm integr...

The aim of this paper is solving nonlinear Volterra-Fredholm fractional integro-differential equations with mixed boundary conditions‎. ‎The basic idea is to convert fractional integro-differential equation to a type of second kind Fredholm integral equation‎. ‎Then the obtained Fredholm integral equation will be solved with Nystr"{o}m and Newton-Kantorovitch method‎.  ‎Numerical tests for demo...

Abstract. In this paper, existence and uniqueness theorems for nonlinear fuzzy fractional Fredholm integro-differential equations are investigated. We interpret Fredholm integro-differential equations under fractional generalized Hukuhara derivatives in the Caputo sense, and for this interpretation, we prove existence results in two type of differentiability. Moreover, two examples are given to...

The spline collocation method  is employed to solve a system of linear and nonlinear Fredholm and Volterra integro-differential equations. The solutions are collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula. We obtain the unique solution for linear and nonlinear system $(nN+3n)times(nN+3n)$ of integro-differential equations. This approximation reduces th...

in this paper, an effective numerical method is introduced for the treatment of nonlinear two-dimensional volterra-fredholm integro-differential equations. here, we use the so-called two-dimensional block-pulse functions.first, the two-dimensional block-pulse operational matrix of integration and differentiation has been presented. then, by using this matrices, the nonlinear two-dimensional vol...

in this paper, a numerical solution for a system of linear fredholm integro-differential equations by means of the sinc method is considered. this approximation reduces the system of integro-differential equations to an explicit system of algebraic equations. the exponential convergence rate $o(e^{-k sqrt{n}})$ of the method is proved. the analytical results are illustrated with numerical examp...