In this paper, we develop the Differential Transform (DT) method in a new scheme to solve the two-dimensional Fredholm integral equations (2D-FIEs) of the second kind. The differential transform method is a procedure to obtain the coefficients of the Taylor expansion of the solution of differential and integral equations. So, one can obtain the Taylor expansion of the solution of arbitrary order and hence the solution of the given equation can be obtained with required accuracy. Here, we first give some basic definitions and properties about DT from references, and then we prove some theorems to extend the DT method for solving the 2D-FIEs. Then by using the DT, the 2D-FIE is converted to a system of linear algebraic equations whose unknowns are the coefficients of the Taylor expansion of the solution. Solving the system gives us an approximate solution. Finally, we give some examples to show the accuracy and efficiency of the presented method.
Ziyaee, F. and Tari, A.
Differential Transform Method for Solving the Two-dimensional Fredholm Integral Equations,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 10,
2, Article 14.
Available at: https://digitalcommons.pvamu.edu/aam/vol10/iss2/14