What is it about?
This paper attempts to propose and investigate a modification of the homotopy perturbation method (MHPM) to study hypersingular integral equations of the first kind. Along with considering this matter, of course , the novel method has been compared with the standard homotopy perturbation method. This method can be conveniently fast to get the exact solutions. The validity and reliability of the proposed scheme are discussed. The MHPM has been discovered to be the significant ideal tool in dealing with the complicated function-theoretic analytical structures within an analytical method.
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Why is it important?
We solve a family of hypersingular integral equations as a model which can be found in mechanical engineering by applying the modified homotopy perturbation method. The proposed scheme is able to solve this kind of integral equations in a satisfactory way.
Perspectives
This article has been communicated with the designer of the homotopy perturbation method who is a well-known scientist in the filed of engineering and applied mathematics. He has confirmed the work and I hole the results of this paper is useful for all researchers who are working in the related subjects.
Dr. Mohammad Ali Fariborzi Araghi
Islamic Azad University
Read the Original
This page is a summary of: Hypersingular integral equations of the first kind: A modified homotopy perturbation method and its application to vibration and active control, Journal of Low Frequency Noise Vibration and Active Control, February 2019, SAGE Publications,
DOI: 10.1177/1461348419827378.
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