Solution of Cauchy type singular integral equations of the first kind by using differential transform method

• Cauchy type singular integral equation over a finite interval is solved.
• Differential transform method is used.
• Degenerate and convolution kernels are considered.
• Numerical results are given.

The differential transform method is extended to solve the Cauchy type singular integral equations (CSIEs) over a finite interval. New theorems for transformation of Cauchy singular integrals are given with proofs. Approximate solutions of CSIEs with two types of kernels, Degenerate and convolution, are obtained. The system of linear equations for characteristic equation is solved analytically. Numerical results are shown to illustrate the efficiency and accuracy of the present method.