Semi-bounded solutions of singular integral equations of Cauchy type - Nik Long, Nik Mohd Asri; Eshkuvatov, Zainidin K.; Mahiub, Mohammad Abdulkawi (Hikari Ltd, 2009)
In this work, semi-bounded numerical solutions of the Cauchy type singular integral equations of the first kind over the interval [−1, 1] is presented. In the integral equation, the truncated Chebyshev series of the third kind Vj and fourth kind Wj with the weight functions ω1(x) = (1 + x)1/2(1 − x)−1/2 and ω2(x) = (1 + x)−1/2(1 − x)1/2, respectively,are used to approximate the unknown function. The exactness of the method is shown for characteristic singular integral equation when the forcing function is linear. The numerical results are given to show the efficiency and accuracy of the method presented.