@Article{cmes.2010.055.191,
AUTHOR = {M. A. Kelmanson and M. C. Tenwick},
TITLE = {Error Reduction in Gauss-Jacobi-Nyström Quadraturefor Fredholm Integral Equations of the Second Kind},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {55},
YEAR = {2010},
NUMBER = {2},
PAGES = {191--210},
URL = {http://www.techscience.com/CMES/v55n2/25457},
ISSN = {1526-1506},
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 theoretical framework of the new technique is developed, implemented and validated on test problems with known exact solutions, and degenerate cases of the new Gauss-Jacobi scheme are corroborated against standard Gauss-Legendre and first- and second-kind Gauss-Chebyshev methods (i.e. using tabulated weights and abscissae). Significant error reductions over standard methods are observed, and all results are explained in the context of the new theory.},
DOI = {10.3970/cmes.2010.055.191}
}