In this article, we apply the operational matrix to find the numerical solution of two- dimensional nonlinear Volterra integro-differential equation (2DNVIDE). Form this prospect, two-dimensional shifted Legendre functions (2DSLFs) has been presented for integration, product as well as differentiation. This method converts 2DNVIDE to an algebraic system of equations, so the numerical solution o...

s of PhD Theses at Irish Universities 2007 On the Asymptotic Behaviour of Deterministic and Stochastic Volterra Integro–Differential Equations

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...

Abstract. In this study we developed and modified Taylor expansion method for approximating the solution of linear Fredholm and Volterra integro-differential equations. Via Taylor’s expansion of the unknown function at an arbitrary point, the integro-differential equations to be solved is approximately transformed into a system of linear equations for the unknown and its derivatives which can b...

This study outlines the local fractional integro-differential equations carried out by the local fractional calculus. The analytical solutions within local fractional Volterra and Abel’s integral equations via the Yang-Laplace transform are discussed. Some illustrative examples will be discussed. The obtained results show the simplicity and efficiency of the present technique with application t...