Abstract—In this paper, numerical solution of system of Fredholm and Volterra integral equations by means of the Spline collocation method is considered. This approximation reduces the system of integral equations to an explicit system of algebraic equations. The solution is collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula. The error analysis of propose...

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...

In this paper, we establish a sufficient condition for the controlla-bility of impulsive quasi-linear fractional mixed Volterra-Fredholm-type inte-grodifferential equations in Banach spaces. The results are obtained by using Banach contraction fixed point theorem combined with the fractional calculus theory.

The purpose of this study is to present an approximate numerical method for solving high order linear Fredholm-Volterra integro-differential equations in terms of rational Chebyshev functions under the mixed conditions. The method is based on the approximation by the truncated rational Chebyshev series. Finally, the effectiveness of the method is illustrated in several numerical examples. The p...

In this paper, a numerical method for solving the Fredholm and Volterra integral equations is presented. The method is based upon the second Chebyshev wavelet approximation. The properties of the second Chebyshev wavelet are first presented and then operational matrix of integration of the second Chebyshev wavelets basis and product operation matrix of it are derived. The second Chebyshev wavel...

In this paper, we will compare a Homotopy perturbation algorithm and Taylor series expansin method for a system of second kind Fredholm integral equations. An application of He’s homotopy perturbation method is applied to solve the system of Fredholm integral equations. Taylor series expansin method reduce the system of integral equations to a linear system of ordinary differential equation.

In 1982, Dubois and Prade [4, 5] first introduced the concept of integration of fuzzy functions. Kaleva [7] studied the measurability and integrability for the fuzzy set-valued mappings of a real variable whose values are normal, convex, upper semicontinuous, and compactly supported by fuzzy sets in Rn. Existence of solutions of fuzzy integral equations has been studied by several authors [1, 2...