A Hybrid Method for All Types of Solutions of the System of Cauchy-Type Singular Integral Equations of the First Kind

H. X. Mamatova (), Z. K. Eshkuvatov () and Sh. Ismail ()
Additional contact information
H. X. Mamatova: Faculty of Ocean Engineering Technology and Informatics, University Malaysia Terengganu (UMT), Kuala Terengganu 21030, Malaysia
Z. K. Eshkuvatov: Faculty of Ocean Engineering Technology and Informatics, University Malaysia Terengganu (UMT), Kuala Terengganu 21030, Malaysia
Sh. Ismail: Faculty of Science and Technology, Universiti Sains Islam Malaysia (USIM), Bandar Baru Nilai 71800, Malaysia

Mathematics, 2023, vol. 11, issue 20, 1-30

Abstract: In this note, the hybrid method (combination of the homotopy perturbation method (HPM) and the Gauss elimination method (GEM)) is developed as a semi-analytical solution for the first kind system of Cauchy-type singular integral equations (CSIEs) with constant coefficients. Before applying the HPM, we have to first reduce the system of CSIEs into a triangle system of algebraic equations using GEM, which is then carried out using the HPM. Using the theory of the bounded, unbounded and semi-bounded solutions of CSIEs, we are able to find inverse operators for the system of CSIEs of the first kind. A stability analysis and convergent of the proposed method has been conducted in the weighted L p space. Moreover, the proposed method is proven to be exact in the Holder class of functions for the system of characteristic SIEs for any type of initial guess. For each of the four cases, several examples are provided and examined to demonstrate the proposed method’s validity and accuracy. Obtained results are compared with the Chebyshev collocation method and modified HPM (MHPM). Example 3 reveals that the error term of the MHPM is slightly superior to that of the HPM. One of the features of the proposed method is that it can be solved as a complex-valued system of CSIEs. Numerical results revealed that the hybrid method dominates others.

Keywords: hybrid method; cauchy-type singular integral equations; gauss elimination method; homotopy perturbation method; stability; convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/20/4404/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/20/4404/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:20:p:4404-:d:1265730

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().