‎we study dual integral equations which appear in formulation of the‎ ‎potential distribution of an electrified plate with mixed boundary‎ ‎conditions‎. ‎these equations will be converted to a system of‎ ‎singular integral equations with cauchy type kernels‎. ‎using‎ ‎chebyshev polynomials‎, ‎we propose a method to approximate the‎ ‎solution of cauchy type singular integral equation which will ...

Abstract This work introduces a new integral transform for functions of exponential order called “NE transform”. We prove some properties NE -transform. Also, applications the NE- to find solution ordinary linear equation are given. The relationships with well-known transforms characterized by identities. study this transform. Then we compare it few exiting in Laplace family such as Laplace, Su...

We propose an efficient computation method for an infinite integral ∞ 0 xdx/(1 + x 6 sin 2 x), which has an unbounded integrand with highly oscillated singularity. Computing the value of this integral has been a problem since 1984. We herein demonstrate that the method using the Hilbert transform to change this type of singular function into a smooth function and compute the value of the integr...