The fast solution of periodic pseudodifferential equations

Applicable Analysis

Volumn 63, Issue 1-2, 1996, Pages 3-23

  Berthold, D ^a   Silbermann, B ^a  

^a NONE

Author keywords

Approximation method; Fast fourier transormation; Periodic pseudodifferential equation

Indexed keywords

EID: 0342489427     PISSN: 00036811     EISSN: 1563504X     Source Type: Journal    
DOI: 10.1080/00036819608840493     Document Type: Article

References (19)

1. Amosov, B.A., 1990. On the approximate solution of elliptic pseudodifferential equations on a smooth closed curve. 9: 545–563. ZFAA
2. Berthold, D., Hoppe, W., and Silbermann, B., 1992. A fast algorithm for solving the generalized airfoil equation. J. Comp. Appl. Math., 43: 185–219.
3. Berthold D., Silbermann B., Corrected collocation methods for periodic pseudodifferential equations Numer. Math., to appear.
4. Chandler, G.A., and Sloan, I.H., 1990. Spline qualocation mehtods for boundary integral equations. Numer. Math., 58: 537–567.
5. Hackbusch, W., 1981. Die schnelle Auflösung der Fredholmschen Integralgleichung zweiter Art. Beitr. Num. Math., 9: 47–62.
6. Hackbusch, W., 1985. Multigrid methods and applications, Berlin: Springer-Verlag.
7. Hagen, R., and Silbermann, B., “ On the stability of the qualocation method, Sem. Anal. Oper. Eq. ”. In K.-Weierstraβ—Inst. Math. 43–52. Berlin
8. Hagen, R., and Silbermann, B., 1989. A Banach Algebra approach to the stability of projections methods for singular integral equations. Math. Nachr., 140: 285–297.
9. Hagen, R., and Silbermann, B., “ On the convergence of the qualocation method ”. In FB Math., Techn. Univ. Chemnitz Preprint Nr.
10. Mclean, W., and Wendland, W.L., 1989. Trigonometric approximation of solutions of periodic pseudodifferential equations. Oper.Th.: Advances and Applications, 41: 359–383.
11. Pröβdorf, S., 1978. Some classes of singular equations, Amsterdam: North-Holland Publ.Comp. New York, Oxford
12. p 6: 539–558. (German), ZfAA
13. Prödorf, S., and Silbermann, B., 1977. “ Projection methods and the approximate solution of singular equations ”. In BSB B.G. Teubner Verlagsges, Leipzig. (German)
14. Pröβdorf, S., and Silbermann, B., 1991. Numerical analysis for integral and related operator equations, Berlin: Akademie-Verlag. Birkhäuser-Verlag Basel 1991
15. Schippers, H., “ Multiple grid methods for equation of the second kind with appliction in fluid mechanics ”. In Math. Centre Tracts
16. Schmidt, G., 1983. On spline collocation for singular integral equations. Math. Nachr., 111: 177–196.
17. Schmidt, G., 1984. The convergence of Galerkin and collocation methods with splines for pseudodifferential equations on closed curves. ZFAA, 3: 371–384.
18. Sloan, I.H., 1988. A quadrature-based approach to improving the collocation method. Numer. Math., 54: 41–56.
19. Sloan, I.H., and Wendland, W.L., 1989. A quadrature-based approach to improving the collocation method for splines of even degree. ZfAA, 8: 361–376.