Complex variable formulations for usual and hypersingular integral equations for potential problems???with applications to corners and cracks

1996 ◽  
Vol 17 (5) ◽  
pp. 279-286
Author(s):  
R. Kolhe ◽  
W. Ye ◽  
C.-Y. Hui ◽  
S. Mukherjee
Keyword(s):  
Integral Equations ◽  
Complex Variable ◽  
Hypersingular Integral ◽  
Hypersingular Integral Equations ◽  
Potential Problems

scholarly journals Hypersingular integral equations of the first kind: A modified homotopy perturbation method and its application to vibration and active control

2019 ◽  
Vol 38 (2) ◽  
pp. 706-727 ◽  
Author(s):  
Reza Novin ◽  
Mohammad Ali Fariborzi Araghi
Keyword(s):  
Perturbation Method ◽  
Integral Equations ◽  
Homotopy Perturbation Method ◽  
The Novel ◽  
Validity And Reliability ◽  
Hypersingular Integral ◽  
Homotopy Perturbation ◽  
Hypersingular Integral Equations ◽  
Ideal Tool ◽  
Novel Method

This paper attempts to propose and investigate a modification of the homotopy perturbation method 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. Different examples are included to prove so. According to the results, we further state that new simple homotopy perturbation method is so efficient and promises the exact solution. The modification of the homotopy perturbation method 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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