Abstract
In this paper a 1-D singular integral equation motivated by the well-known singular volume integral equation associated with electromagnetic interior scattering is considered. In the 3-D case the kernel (the dyad Green’s function) is O(R−3) and in the present 1-D case the kernel is O(R−1). The numerical solution is obtained by using a simple Nystrom method. The mapping properties of the integral operator and the numerical integral operators are studied in various (Holder) subspaces of C([a, b]). Convergence theorems for the numerical integral operators as well as for the numerical solutions are proved.
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