Spectral homotopy analysis method for solving nonlinear Volterra integro differential equations

In this paper we proposed Spectral Homotopy analysis method to solve nonlinear Volterra integro-differential equations. Some examples are given to approve the efficiency and the accuracy of the proposed method. The SHAM results show that the proposed approach is quite reasonable when compared to homotopy analysis method and exact analytical solutions

(SI10-077) A Novel Collocation Method for Solving Second-order Volterra Integro-differential Equations

In this article, we present an efficient numerical methodology to solve second-order linear Volterra integro-differential equations. Further, the modified Chebyshev collocation method is used at the Gauss-Lobatto collocation points. In that context, some theoretical investigation related to error analysis is suggested through residual function. Numerical examples are also encountered to study the applicability of the present method. In order to get a vivid illustration of the efficiency, we present a comparative survey with three existing collocation methods

A novel collocation method based on residual error analysis for solving integro-differential equations using hybrid Dickson and Taylor polynomials

In this study, a novel matrix method based on collocation points is proposed to solve some linear and nonlinear integro-differential equations with variable coefficients under the mixed conditions. The solutions are obtained by means of Dickson and Taylor polynomials. The presented method transforms the equation and its conditions into matrix equations which comply with a system of linear algebraic equations with unknown Dickson coefficients, via collocation points in a finite interval. While solving the matrix equation, the Dickson coefficients and the polynomial approximation are obtained. Besides, the residual error analysis for our method is presented and illustrative examples are given to demonstrate the validity and applicability of the method

A Taylor collocation method for the solution of linear integro-differential equations

In this study, a matrix method called the Taylor collocation method is presented for numerically solving the linear integro-differential equations by a truncated Taylor series. Using the Taylor collocation points, this method transforms the integro-differential equation to a matrix equation which corresponds to a system of linear algebraic equations with unknown Taylor coefficients. Also the method can be used for linear differential and integral equations. To illustrate the method, it is applied to certain linear differential, integral, and integro-differential equations and the results are compared