In this paper the method of integral equations is proposed for some problems of electrical engineering ( current density, radiative heat transfer, heat conduction). Presented models lead to a system of Fredholm integral equations, integro-differential equations or Volterra-Fredholm integral equations, respectively. We propose various numerical methods (discretization method and projection metho...

‎‎‎‎‎‎‎‎‎‎‎‎‎This paper aims to construct a general formulation for the shifted Jacobi operational matrices of integration and product‎. ‎The main aim is to generalize the Jacobi integral and product operational matrices to the solving system of Fredholm and Volterra integro--differential equations‎ which appear in various fields of science such as physics and engineering. ‎The Operational matr...

An efficient hybrid method is developed to approximate the solution of the high-order nonlinear Volterra-Fredholm integro-differential equations. The properties of hybrid functions consisting of block-pulse functions and Lagrange interpolating polynomials are first presented. These properties are then used to reduce the solution of the nonlinear Volterra-Fredholm integro-differential equations ...

This paper describes an approximating solution, based on Lagrange interpolation and spline functions, to treat functional integral equations of Fredholm type and Volterra type. This method can be extended to functional differential and integro-differential equations. For showing efficiency of the method we give some numerical examples.

In this paper, we employed the use of Standard Integral Collocation Approximation Method to obtain numerical solutions of special higher orders linear Fredholm-Volterra Integro-Differential Equations. Power Series, Chebyshev and Legendre's Polynomials forms of approximations are used as basis functions. From the computational view points, the method is efficient, convenient, reliable and superi...

This paper is concerned with obtaining the approximate solution of Fredholm-Volterra integro-differential equations. Properties of the Shannon wavelets and connection coefficients are first presented. We design a numerical scheme for these equations using the Galerkin method incorporated with the Shannon wavelets approximation and the connection coefficients. We will show that using this techni...

Abstract— A new polynomial method to solve Volterra–Fredholm Integral equations is presented in this work. The method is based upon Shifted Legendre Polynomials. The properties of Shifted Legendre Polynomials and together with Gaussian integration formula are presented and are utilized to reduce the computation of Volterra–Fredholm Integral equations to a system of algebraic equations. Some num...

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...

Some New Uniqueness Results of Solutions for Fractional Volterra-Fredholm Integro-Differential Equations