Abstract
In this paper, we develop a method for evaluating one dimensional singular integrals (weakly, strongly, and hyper-singular) that converge in the sense of Cauchy principal value and Hadamard finite part integrals. A proof of convergence of this method is also provided.
Highlights
Open AccessMany problems in engineering and science require evaluating singular integrals.The problem considered in this paper is of practical interest in many areas
We develop a method for evaluating one dimensional singular integrals that converge in the sense of Cauchy principal value and Hadamard finite part integrals
The one dimensional singular integrals are defined in the literature as follows b u(t) ∫a (t − s)p dt, s ∈(a,b), p > 0, (1)
Summary
How to cite this paper: Tran, N.T. (2017) Simple Method for Evaluating Singular Integrals. How to cite this paper: Tran, N.T. (2017) Simple Method for Evaluating Singular Integrals. American Journal of Computational Mathematics, 7, 444-450. Received: November 12, 2017 Accepted: December 11, 2017 Published: December 14, 2017
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