Abstract
In this paper, a modified algorithm is proposed for solving linear integro-differential equations of the second kind. The main idea is based on applying Romberg extrapolation algorithm (REA), on Trapezoidal rule. In accordance with the computational perspective, the comparison has shown that Adomian decomposition approach is more effective to be utilized. The numerical results show that the modified algorithm has been successfully applied to the linear integro-differential equations and the comparisons with some existing methods appeared in the literature reveal that the modified algorithm is more accurate and convenient.
Highlights
Mathematical modelling of real-life problems usually results in functional equations, such as differential, integral, and integro-differential equations
The numerical results show that the modified algorithm has been successfully applied to the linear integro-differential equations and the comparisons with some existing methods appeared in the literature reveal that the modified algorithm is more accurate and convenient
The numerical solution of integro-differential equation is a part of numerical analysis, which has been changed by the ongoing revolution in numerical methods
Summary
Mathematical modelling of real-life problems usually results in functional equations, such as differential, integral, and integro-differential equations. Results show that the variation iteration method (VIM) has been successfully employed to obtain the approximate analytical solutions of the nonlinear integro-differential equations Others solve it through a comparison of the Adomian decomposition method and the wavelet-Galerkin method [20]. Saadati et al [1], presented numerical method to approximate the integrodifferential equations (Volterra, Fredholm) using the Trapezoidal rule This method based on transforming the first derivative integro-differential equations to a system of algebraic equations. Many studies have indicated the variational iteration method to solve the linear and nonlinear integro differential equations (Volterra, Fredholm) [3] [14] [15] [16] [17] They applied the variational iteration method to approximate the solutions of the integro-differential equations.
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