TY  - EJOU
AU  - Kelmanson, M. A. 

TI  - Error Reduction in Gauss-Jacobi-Nyström Quadraturefor Fredholm Integral Equations of the Second Kind
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2010
VL  - 55
IS  - 2
SN  - 1526-1506

AB  - 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.
KW  - Fredholm integral equations
KW  -  Nyström method
KW  -  numerical quadrature
KW  -  Gauss-Jacobi polynomials
KW  -  error analysis

DO  - 10.3970/cmes.2010.055.191