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Introduction. We consider an interpolation scheme based on piecewise polynomials with continuous first derivatives and the Gaussian points as interpolation points. A collocation method based on this interpolation scheme is applied to oneand twodimensional Fredholm equations of the second kind. This scheme has been applied to a collocation method by de Boor and Swartz [4] and Houstis [9] for the numerical solution of ordinary differential equations. Also, Douglas and Dupont [6], [7], [8] and Houstis [10], [11] have studied a collocation method for partial differential equations based on the above scheme. A survey of numerical methods for the solution of Fredholm integral equations of the second kind is given by Atkinson [1]. In Part I we present the formulation and error analysis of the interpolation scheme. In Part II we apply this scheme to the solution of Fredholm integral equations of the second kind and give an experimental comparison with Nyström's method.

A collocation method for Fredholm integral equations of the second kind