Asymptotic error expansion of two-dimensional Volterra integral equation by iterated collocation
Applied Mathematics and Computation
Solving partial differential equations by two-dimensional differential transform method
Applied Mathematics and Computation
Applied Mathematics and Computation
On solving the initial-value problems using the differential transformation method
Applied Mathematics and Computation
Two-dimensional differential transform for partial differential equations
Applied Mathematics and Computation
On solving some eigenvalue problems by using a differential transformation
Applied Mathematics and Computation
Different applications for the differential transformation in the differential equations
Applied Mathematics and Computation
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The differential transformation method provides an iterative procedure to obtain the spectrum of analytic solutions. In this paper we extend the differential transformation approach for the solution of two-dimensional integral equations. We give some basic properties and a new differential transformation-type method for the solution of linear and nonlinear two-dimensional Volterra integral equations. By extension of the operations, a two-dimensional integral equation in the domain of interest can be transformed into an algebraic equation in the domain K, H. We show that, after transforming the original equation into an algebraic equation, the coefficients W(k, h) for k, h=1, 2,... are determined and then, by substituting the values of W(k, h) in the transformed equation, the closed form solution of the original equation can be obtained. The reliability and efficiency of the proposed scheme are demonstrated by numerical experiments.