The Journal of the Australian Mathematical Society. Series B. Applied Mathematics

Research Article

A piecewise polynomial approximation to the solution of an integral equation with weakly singular kernel

G. Vainikkoa1 and P. Ubaa1

a1 Department of Applied Mathematics, Tartu State University, 202 400, Tartu, Liivi 2, U.S.S.R.


We construct collocation methods with an arbitrary degree of accuracy for integral equations with logarithmically or algebraically singular kernels. Superconvergence at collocation points is obtained. A grid is used, the degree of non-uniformity of which is in good conformity with the smoothness of the solution and the desired accuracy of the method.

(Received July 22 1980)

(Revised February 05 1981)