Applied Mathematics and Computation
Taylor polynomial solutions of nonlinear Volterra-Fredholm integral equations
Applied Mathematics and Computation
Variational iteration method: New development and applications
Computers & Mathematics with Applications
Variational iteration method for solving integral equations
Computers & Mathematics with Applications
International Journal of Computer Mathematics
Computers & Mathematics with Applications
The numerical solution of the non-linear integro-differential equations based on the meshless method
Journal of Computational and Applied Mathematics
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In this study it is shown that the numerical solutions of linear Fredholm integro-differential equations obtained by using Legendre polynomials can also be found by using the variational iteration method. Furthermore the numerical solutions of the given problems which are solved by the variational iteration method obviously converge rapidly to exact solutions better than the Legendre polynomial technique. Additionally, although the powerful effect of the applied processes in Legendre polynomial approach arises in the situations where the initial approximation value is unknown, it is shown by the examples that the variational iteration method produces more certain solutions where the first initial function approximation value is estimated. In this paper, the Legendre polynomial approximation (LPA) and the variational iteration method (VIM) are implemented to obtain the solutions of the linear Fredholm integro-differential equations and the numerical solutions with respect to these methods are compared.