approximate solution of magnetic boundary value problems‎ ‎in‎ ‎geometrically‎ ‎complex‎ ‎domains using the‎ ‎method of‎ ‎integral equation systems

‎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.