Approximate Solution of Magnetic Boundary Value Problems‎ ‎in‎ ‎Geometrically‎ ‎Complex‎ ‎Domains Using the‎ ‎Method of‎ ‎Integral Equation Systems

Document Type : Original Scientific Paper

Authors

1 ‎Department of General and Applied Mathematics,‎ ‎Azerbaijan State Oil and Industry University, ‎Baku‎, ‎Azerbaijan

2 ‎Department of Mathematics, University of Igdir,‎ ‎Igdir‎, ‎Türkiye

10.22052/mir.2025.257320.1531

Abstract

‎This paper provides a rigorous theoretical justification for the collocation method applied to a system of integral equations arising in magnetic boundary value problems governed by the vector Helmholtz equation‎. ‎At appropriately selected collocation points‎, ‎the system of integral equations is transformed into a system of algebraic equations‎, ‎for which the existence and uniqueness of solutions are rigorously established‎. ‎The convergence of the algebraic solutions to the exact solution of the integral equations is proven‎, ‎and the convergence rate of the method is analytically derived‎. ‎Furthermore‎, ‎within the framework of the proposed approach‎, ‎explicitly constructed sequences are rigorously proven to converge to the exact solution of the considered magnetic boundary value problems‎, ‎thereby providing a systematic and reliable approximation scheme‎.

Keywords

Main Subjects

References

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Mathematics Interdisciplinary Research
Volume 10, Issue 4
In Progress
December 2025
Pages 407-430

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