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On spline collocation for convolution equations

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Abstract

We consider the numerical solution of Wiener-Hopf integral equations and Mellin convolution equations by collocation methods and their iterated and discrete variants, using piecewise polynomials as basis functions. In the present paper we obtain results on stability and optimal convergence in the Lp norm generalizing those of [4]–[6] and [9].

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References

  1. Anselone, P. M. and I. H. Sloan: Integral equations on the half-line. J. Integral Equations 9(Suppl.) (1985), 3–23.

    Google Scholar 

  2. Atkinson, K. E.: A survey of numerical methods for the solution of Fredholm integral equations of the second kind. SIAM, Philadelphia, 1976.

    Google Scholar 

  3. Brunner, H. and P. J. van der Houwen: The numerical solution of Volterra equations. North-Holland, Amsterdam 1986.

    Google Scholar 

  4. Chandler, G. A. and I. G. Graham: The convergence of Nyström methods for Wiener-Hopf equations. Numer. Math. 52 (1988), 345–364.

    Google Scholar 

  5. Chandler, G. A. and I. G. Graham: Higher order methods for linear functionals of solutions of second kind equations. SIAM J. Numer. Anal. (to appear).

  6. Chandler, G. A. and I. G. Graham: Product integration-collocation methods for non-compact integral operator equations. Math. Comp. 50 (1988), 125–138.

    Google Scholar 

  7. Clancey, K. and I. Gohberg: Factorization of matrix functions and singular integral operators. Birkhäuser, Basel, 1981.

    Google Scholar 

  8. Elschner, J.: Asymptotics of solutions to pseudodifferential equations of Mellin type. Math. Nachr. 130 (1987), 267–305.

    Google Scholar 

  9. Elschner, J.: On spline approximation for a class of non-compact integral equations. Math. Nachr. (to appear).

  10. Gohberg, I. C. und I. A. Feldman: Convolution equations and projection methods for their solution. Amer. Math. Soc., Providence, 1974.

    Google Scholar 

  11. Prößdorf, S. and A. Rathsfeld: Mellin techniques in the numerical analysis of one-dimensional singular integral equations. Preprint P-MATH-06/88, Karl-Weierstraß-Inst. Math. Akad. Wiss. DDR, Berlin, 1988.

    Google Scholar 

  12. Rathsfeld, A.: Eine Quadraturformelmethode für Mellin-Operatoren nullter Ordnung. Math. Nachr. 137 (1988), 321–354.

    Google Scholar 

  13. Sloan, I. H. and A. Spence: Projection methods for integral equations on the half-line. IMA J. Numer. Anal. 6 (1986), 153–172.

    Google Scholar 

  14. Vainikko, G., A. Pedas and P. Uba: Methods for solving weakly singular integral equations (Russian). Gos. Univ. Tartu, 1984.

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  1. Karl-Weierstrass-Institut für Mathematik, Akadem. der Wiss. der DDR, Mohrenstrasse 39, 1086, Berlin, DDR

    Johannes Elschner

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  1. Johannes Elschner
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Elschner, J. On spline collocation for convolution equations. Integr equ oper theory 12, 486–510 (1989). https://doi.org/10.1007/BF01199456

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