Approximate solution of bisingular integro-differential equations (Q686854)

In the literature collocation and Galerkin methods have been used to obtain approximate solutions of bisingular integro-differential equations. In this paper the author develops a class of special para- algebras in a Banach algebra setting to reduce the problem of the applicability of collocation and Galerkin methods to the investigation of the invertibility of certain elements in a quotient para-algebra. He solves this problem by using a local principle for para-algebras which generalizes the well-known local principle of Gohberg-Krupnik.