Abstract
In this paper, the differential transformation method is applied to the system of Volterra integral and integrodifferential equations with proportional delays. The method is useful for both linear and nonlinear equations. By using this method, the solutions are obtained in series forms. If the solutions of the problem can be expanded to Taylor series, then the method gives opportunity to determine the coefficients of Taylor series. Hence, the exact solution can be obtained in Taylor series form. In illustrative examples, the method is applied to a few types of systems.
Highlights
Integral and integrodifferential equations have found applications in engineering, physics, chemistry, and insurance mathematics [1,2,3]
The linear and nonlinear systems of integrodifferential equations have been solved by Haar functions [5]; Maleknejad and Tavassoli Kajani [6] used the hybrid Legendre functions, the Chebyshev polynomial method [7], the Bessel collocation method [8, 9], the Taylor collocation method [10], the homotopy perturbation method [11, 12], the variational iteration method [13], the differential transformation method [14], and the Taylor series method [15]
Biazar et al [16] have obtained the solutions of systems of Volterra integral equations of the first kind by the Adomian method
Summary
Integral and integrodifferential equations have found applications in engineering, physics, chemistry, and insurance mathematics [1,2,3]. There are a lot of methods of approach for solutions of systems of integral and integrodifferential equations. Biazar et al [16] have obtained the solutions of systems of Volterra integral equations of the first kind by the Adomian method. The homotopy perturbation method has been used for systems of Abel’s integral equations [17]. The special systems of integral equations have been solved by the differential transformation method [18]. The nonlinear systems of Volterra integrodifferential equations with delay arguments have been studied by Yalcınbas and Erdem [20]. We consider the system of Volterra integral and integrodifferential equations with proportional delays: rx.
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