An extrapolation method for a class of boundary integral equations

Mathematics of Computation

Volumn 65, Issue 214, 1996, Pages 587-610

  Xu, Yuesheng ^a   Zhao, Yunhe ^a  

^a NORTH DAKOTA STATE UNIVERSITY   (United States)

Author keywords

Asymptotic expansion; Boundary integral equations; Boundary value problem; Euler Maclaurin formula; Extrapolation scheme; Nystr m method; Periodic logarithmic Fredholm integral equations

Indexed keywords

ASYMPTOTIC EXPANSION; BOUNDARY INTEGRAL METHOD; CONVERGENCE ACCELERATION; EXTRAPOLATION; FREDHOLM EQUATION; KERNEL FUNCTION; LOGARITHMIC FUNCTION; PERIODIC FUNCTION;

CONVERGENCE OF NUMERICAL METHODS; INTEGRAL EQUATIONS;

BOUNDARY VALUE PROBLEMS;

EID: 0030367032     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-96-00723-5     Document Type: Article

References (14)

1. P. M. Anselone, Collectively Compact Operator Approximation Theory and Applications to Integral Equations, Prentice-Hall, Englewood Cliffs, N.J., 1971. MR 56:1753
2. K. E. Atkinson, The numerical solution of Fredholm integral equations of the second kind with singular kernels, Numer. Math. 19 (1972), 248-259. MR 46:6632
3. K. E. Atkinson, A Survey of Numerical Methods for the Solution of Fredholm Integral Equations of the Second Kind, SIAM, 1976. MR 58:3577
4. K. E. Atkinson, A survey of boundary integral equation methods for the numerical solution of Laplace's equation in three dimensions, in Numerical Solutions of Integral Equations, (Edited by Michael A. Golberg), Plenum, 1990. MR 91j:65169
5. K. E. Atkinson and G. Chandler, Boundary integral equation methods for solving Laplace's equation with nonlinear boundary conditions: the smooth boundary case, Math. Comp. 55 (1990), 451-472. MR 91d:65181
6. P. J. Davis and P. Rabinowitz, Methods of Numerical Integration, 2nd Edition, Academic Press, San Diego, 1984. MR 86d:65004
7. W. F. Ford and A. Sidi, An algorithm for a generalization of the Richardson extrapolation process, SIAM J. Numer. Anal. 24 (1987), 1212-1232. MR 89a:65006
8. L. Navot, An extension of the Euler-Maclaurin summation formula to functions with a branch singularity, J. Math. and Phys. 40 (1961), 271-276. MR 25:4290
9. L. Navot, A further extension of the Euler-Maclaurin summation formula, J. Math. and Phys. 41 (1962), 155-163.
10. K. Ruotsalainen and W. Wendland, On the boundary element method for some nonlinear boundary value problems. Numer. Math. 53 (1988), 299-314. MR 89h:65189
11. C. Schneider, Regularity of the solution to a class of weakly singular Fredholm integral equations of the second kind, Int. Eqs. Op. Thy. 2 (1979), 62-68. MR 80f:45002
12. A. Sidi, Comparison of some numerical quadrature formulas for weakly singular periodic Fredholm integral equations, Computing 43 (1989), 159-170. MR 91c:65086
13. A. Sidi and M. Israeli, Quadrature methods for periodic singular and weakly singular Fredholm integral equations, J. Scientific Computing 3 (1988), 201-231. MR 90e:65194
14. I. Sloan, Private communication, 1993.