In this work, we introduce a novel method for solving two-dimensional fuzzy Fredholm integral equations of the second kind (2D-FFIE-2). We use new representation of parametric form of fuzzy numbers and convert a two-dimensional fuzzy Fredholm integral equation to system of two-dimensional Fredholm integral equations of the second kind in crisp case. We can use Adomian decomposition method for n...

In this paper, we propose a new modification of rationalized Haar functions called rationalized Haar s-functions for the numerical solution of linear and nonlinear Volterra integral equations of the second kind. By selecting these functions and following the procedure of determining the wavelet expansion coefficients, the calculations are economized. This method converts the integral equation t...

In this paper, we use the continuous Legendre wavelets on the interval [0,1] constructed by Razzaghi M. and Yousefi S. [6] to solve the linear second kind integral equations. We use quadrature formula for the calculation of the products of any functions, which are required in the approximation for the integral equations. Then we reduced the integral equation to the solution of linear algebraic ...

in this paper, we apply the local fractional laplace transform method (or yang-laplace transform) on volterra integro-differential equations of the second kind within the local fractional integral operators to obtain the analytical approximate solutions. the iteration procedure is based on local fractional derivative operators. this approach provides us with a convenient way to find a solution ...

This work is to provide spectral and pseudo-spectral Jacobi-Galerkin approaches for the second kind Volterra integral equation. The Gauss-Legendre quadrature formula is used to approximate the integral operator and the inner product based on the Jacobi weight is implemented in the weak formulation in the numerical implementation. For some spectral and pseudo-spectral Jacobi-Galerkin methods, a ...

In this paper, we study polynomial spline collocation methods applied to a particular class of integral-algebraic equations of Volterra type. We analyse mixed systems of second and first kind integral equations. Global convergence and local superconvergence results are established.

s of IWANASP, September 10 – 12, 2008, Ericeira, Portugal GENERAL LINEAR METHODS FOR VOLTERRA INTEGRAL EQUATIONS ZDZISÃlAW JACKIEWICZ Departament of Mathematics, Arizona State University Tempe, Arizona 85287, USA E-mail: [email protected] We investigate the class of general linear methods of order p and stage order q = p for the numerical solution of Volterra integral equations of the se...

This work studies the fourth-kind integral equation as a mixed system of first and second-kind Volterra equations(VIEs) with constant delay. Regularity, smoothing properties uniqueness solution this are obtaied by using theorems which give relevant conditions related to VIEs delays. 
 A numerical collocation algorithm on basis piecewise polynomial is designed global convergence proposed me...

In this paper, Adomian method has been applied to approximate the solution of fuzzy volterra-fredholm integral equation. That, by using parametric form of fuzzy numbers, a fuzzy volterra-fredholm integral equation has been converted to a system of volterra-fredholm integral equation in crisp case. Finally, the method is explained with illustrative examples.

‎‎‎In this paper‎, ‎we develop multi-step methods to solve a class of two-dimensional nonlinear Volterra integral equations (2D-NVIEs) of the first kind‎. ‎Here‎, ‎we convert a 2D-NVIE of the first kind to a one-dimensional linear VIE of the first kind and then we solve the resulted equation numerically by multi-step methods‎. ‎We also verify convergence and error analysis of the method‎. ‎At t...