M. A. Kelmanson1 and M. C. Tenwick1
CMES-Computer Modeling in Engineering & Sciences, Vol.55, No.2, pp. 191-210, 2010, DOI:10.3970/cmes.2010.055.191
Abstract A method is presented for improving the accuracy of the widely used Gauss-Legendre Nyström method for determining approximate solutions of Fredholm integral equations of the second kind on finite intervals. The authors' recent continuous-kernel approach is generalised in order to accommodate kernels that are either singular or of limited continuous differentiability at a finite number of points within the interval of integration. This is achieved by developing a Gauss-Jacobi Nyström method that moreover includes a mean-value estimate of the truncation error of the Hermite interpolation on which the quadrature rule is based, making it particularly accurate at low orders. A… More >
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