The Fredholm–Volterra integral equation of the second kind with continuous kernels with respect to position and time, is solved numerically, using the Collocation and Galerkin methods. Also the error, in each case, is estimated.

It has been shown that a normal S-iterative method converges to the solution of a mixed type Volterra-Fredholm functional nonlinear integral equation. Furthermore, a data dependence result for the solution of this integral equation has been proven.

Some existence and uniqueness theorems are established for weakly singular Volterra and Fredholm-Volterra integral equations in C[a, b]. Our method is based on fixed point theorems which are applied to the iterated operator and we apply the fiber Picard operator theorem to establish differentiability with respect to parameter. This method can be applied only for linear equations because otherwi...

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...

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 satised. The nonlinear terms are replaced by its Taylor series. In this technique, the nonlinear Volterra-Fredholm integro...

In this study, a new application of Taylor expansion is considered to estimate the solution of Volterra-Fredholm integral equations (VFIEs) and systems of Volterra-Fredholm integral equations (SVFIEs). Our proposed method is based upon utilizing the nth-order Taylor polynomial of unknown function at an arbitrary point and employing integration method to convert VFIEs into a system of linear equ...

In this paper it is shown that the use of‎ ‎uniform meshes leads to optimal convergence rates provided that‎ ‎the analytical solutions of a particular class of‎ ‎Fredholm-Volterra integral equations (FVIEs) are smooth‎.

We propose a new method, called the textit{the weighted space method}, for the study of the generalized Hyers-Ulam-Rassias stability. We use this method for a nonlinear functional equation, for Volterra and Fredholm integral operators.

In this paper we intend to offer new numerical methods to solvethe fuzzy Fredholm- Volterra integral equations of the firstkind $(FVFIE-1)$. Some examples are investigated to verify convergence results and to illustrate the efficiently of the methods.  

We develop a theoretical context in which to study the future-sequential regularization method developed by J. V. Beck for the Inverse Heat Conduction Problem. In the process, we generalize Beck's ideas and view that method as one in a large class of regularization methods in which the solution of an ill-posed rst-kind Volterra equation is seen to be the limit of a sequence of solutions of well...