Approximate Solution of Magnetic Boundary Value Problems in Geometrically Complex Domains Using the Method of Integral Equation Systems
نویسندگان
1 Department of Mathematics, University of Igdir, Igdir, Türkiye
2 Department of General and Applied Mathematics, Azerbaijan State Oil and Industry University, Baku, Azerbaijan
3 Department of Mathematics, University of Igdir, Igdir, Türkiye
doi
10.22052/mir.2025.257320.1531چکیده
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.
