APPLICATION OF DIFFERENTIAL TRANSFORM METHOD TO THE HYPER-SINGULAR INTEGRAL EQUATIONS

M.A Mahiub

doi:10.12732/ijpam.v112i2.4

Abstract

APPLICATION OF DIFFERENTIAL TRANSFORM METHOD TO THE HYPER-SINGULAR INTEGRAL EQUATIONS

Highlights

Consider the Hyper-singular integral equations (HSIEs) of the form =−1 ψ(t) (t − x)2 dt +K(x, t)ψ(t) dt = f (x), −1 −1 ≤ x ≤ 1, (1)with the conditions ψ(±1) = 0, (2)where K(x, t) is a regular square-integrable function of t and x, f (x) is smooth and ψ is unknown function to be determined
Dutta and Banerjea [11] solved a HSIE in two disjoint intervals using the solution of Cauchy type singular integral equation in disjoint intervals
We present a numerical solution for solving the HSIE(1) using Differential transform method (DTM)

Summary

Introduction

Where K(x, t) is a regular square-integrable function of t and x, f (x) is smooth and ψ is unknown function to be determined. Mahiub et al [6] presented an accurate numerical solution for solving HSIE They used Chebyshev orthogonal polynomials of the second kind for approximating the unknown function. Mandal and Bera [10] discussed an approximate solution for a class of HSIEs. Dutta and Banerjea [11] solved a HSIE in two disjoint intervals using the solution of Cauchy type singular integral equation in disjoint intervals. Dutta and Banerjea [11] solved a HSIE in two disjoint intervals using the solution of Cauchy type singular integral equation in disjoint intervals They used a direct function theoretic method to determine the solution of same HSIE in two disjoint intervals.

Differential Transform Method

Numerical Results

Conclusion