A fast numerical solution method for two dimensional Fredholm integral equations of the second kind

Applied Numerical Mathematics

Volumn 59, Issue 7, 2009, Pages 1709-1719

  Xie, Wen Jing ^a   Lin, Fu Rong ^a  

^a SHANTOU UNIVERSITY   (China)

Author keywords

Approximate matrix; Integral equation; Polynomial interpolation; Residual correction scheme

Indexed keywords

APPROXIMATION ALGORITHMS; INTERPOLATION; LINEAR SYSTEMS; NUMERICAL METHODS; POLYNOMIAL APPROXIMATION; TWO DIMENSIONAL;

APPROXIMATE MATRIX; DISCRETIZATION; FREDHOLM INTEGRAL EQUATIONS; INTERPOLATING POLYNOMIALS; KERNEL FUNCTIONS; MATRIX-VECTOR MULTIPLICATIONS; NUMERICAL SOLUTION METHODS; POLYNOMIAL INTERPOLATION; PRECONDITIONERS; RESIDUAL CORRECTION SCHEME; TWO-DIMENSIONAL INTEGRAL EQUATIONS; VARIABLE FUNCTIONS;

INTEGRAL EQUATIONS;

EID: 63249111441     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2009.01.009     Document Type: Article

References (21)

1. Alpert B., Beylkin G., Coifman R., and Rokhlin V. Wavelets for the fast solution of second-kind integral equations. SIAM J. Sci. Comp. 14 (1993) 159-184
2. Anselone P.M. Collectively Compact Operator Approximation Theory (1971), Prentice-Hall, Englewood Cliffs, NJ
3. Atkinson K.E. A Survey of Numerical Methods for the Solution of Fredholm Integral Equations of the Second Kind (1976), SIAM, Philadelphia, PA
4. Atkinson K.E. The Numerical Solution of Integral Equations of the Second Kind (1997), Cambridge University Press, Cambridge
5. Axelsson O. Iterative Solution Methods (1996), Cambridge University Press, Cambridge
6. Baker C.T. The Numerical Treatment of Integral Equations (1977), Clarendon Press, Oxford
7. Battles Z., and Trefethen L.N. An extension of MATLAB to continuous functions and operators. SIAM J. Sci. Comp. 25 (2004) 1743-1770
8. Beylkin G., Coifman R., and Rokhlin V. Fast wavelet transforms and numerical algorithms I. Comm. Pure Appl. Math. 46 (1991) 141-183
9. Brutman L. Lebesgue functions for polynomial interpolation - a survey. Ann. Numer. Math. 4 (1977) 111-127
10. Delves L.M., and Mohamed J.L. Computational Methods for Integral Equations (1985), Cambridge University Press, New York
11. Farengo R., Lee Y.C., and Guzdar P.N. An electromagnetic integral equation: application to microtearing modes. Phys. Fluids 26 (1983) 3515-3523
12. Golub G., and Van Loan C. Matrix Computations. second ed. (1989), Johns Hopkins University Press, Baltimore
13. Greengard L., and Rokhlin V. A fast algorithm for particle simulations. J. Comput. Phys. 73 (1987) 325-348
14. Greengard L., and Rokhlin V. A new version of the fast multipole method for the Laplace equation in three dimensions. Acta Numerica 6 (1997) 229-269
15. Han G.Q., and Zhang L.Q. Asymptotic error expansion and extrapolation of the Nystrom eethord for two-dimensional Fredholm integral equations. Acta Math. Appl. Sinica 18 2 (1995) 218-224 (in Chinese)
16. Hsu L.C., Zhou Y.S., and Sun Y.B. Approximation Theory (1985), National Defencial Industry Publishing Company, China (in Chinese)
17. Ivanov V.V., and Zadiraka V.K. Some new results in theory of approximation. Computational Mathematics (1966), Kiev University Press, Kiev 30-36 (in Russian)
18. Lin F.R. Preconditioned iterative methods for the numerical solution of Fredholm equations of the second kind. Calcolo 40 (2003) 231-248
19. Tausch J. The variable order fast multipole method for boundary integral equations of the second kind. Computing 72 (2004) 267-291
20. Wang Y., and Xu Y. A fast wavelet collocation method for integral equations on polygons. J. Integral Equations Appl. 17 (2005) 277-330
21. Xia A.S., and Wang L. Iterative corrections for finite element solutions of two dimensional second kind Fredholm integral equations. J. Inst. Command Technology 11 2 (2000) 105-108 (in Chinese)