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| Paper IPM / M / 8519 |
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| Abstract: | |
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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.
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