in this paper, a method for finding an approximate solution of a class of two-dimensional nonlinear volterra integral equations of the first-kind is proposed. this problem is transformedto a nonlinear two-dimensional volterra integral equation of the second-kind. the properties ofthe bivariate shifted legendre functions are presented. the operational matrices of integrationtogether with the produ...

We introduce a new numerical approach for solving Volterra integral equations of the second kind when the kernel contains a mild singularity. We give a convergence result. We also present numerical examples which show the performance and efficiency of our method.

‎‎In this paper, Solvability nonlinear Volterra integral equations with general vanishing delays is stated. So far sinc methods for approximating the solutions of Volterra integral equations have received considerable attention mainly due to their high accuracy. These approximations converge rapidly to the exact solutions as number sinc points increases. Here the numerical solution of nonlinear...

In this paper, the well known iterated Galerkin method and iterated Galerkin-Kantorovich regularization method for approximating the solution of Fredholm integral equations of the second kind are generalized to Hammerstein equations with smooth and weakly singular kernels. The order of convergence of the Galerkin method and those of superconvergence of the iterated methods are analyzed. Numeric...

an ecient method, based on the legendre wavelets, is proposed to solve thesecond kind fredholm and volterra integral equations of hammerstein type.the properties of legendre wavelet family are utilized to reduce a nonlinearintegral equation to a system of nonlinear algebraic equations, which is easilyhandled with the well-known newton's method. examples assuring eciencyof the method and ...

We describe the derivation of order conditions, without restrictions on stage order, for general linear methods for ordinary differential equations. This derivation is based on the extension of Albrecht approach proposed in the context of Runge-Kutta and composite and linear cyclic methods. This approach was generalized by Jackiewicz and Tracogna to two-step Runge-Kutta methods, by Jackiewicz a...

A two-point boundary value problem is considered on the interval [0, 1], where the leading term in the differential operator is a Riemann-Liouville fractional derivative of order 2 − δ with 0 < δ < 1. It is shown that any solution of such a problem can be expressed in terms of solutions to two associated weakly singular Volterra integral equations of the second kind. As a consequence, existence...

M. A. Abdou, Khamis I. Mohamed and A. S. Ismail, On the numerical solutions of Fredholm-Volterra integral equation, Appl. Math. Comp. 146, 713-728, (2003). M. A. Abdou, Khamis I. Mohamed and A. S. Ismail, Toeplitz Matrix and product Nystrom methods for solving the singular integral equation, Le Matematiche LVII-Fasc. I, 21-37, (2002). H. Brunner, On the numerical solution of nonlinear VolterraF...