Product integration-collocation methods for noncompact integral operator equations

摘要: We discuss the numerical solution of a class second-kind integral equations in which operator is not compact. Such arise, for example, when boundary methods are applied to potential problems two-dimensional domain with corners boundary. able prove optimal orders convergence usual collocation and product integration on graded meshes, provided some simple modifications made underlying basis functions. These sufficient ensure stability, but do damage rate convergence. Numerical experiments show that such necessary certain circumstances.