Fast solvers of integral and pseudodifferential equations on closed curves
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Abstract:
On the basis of a fully discrete trigonometric Galerkin method and two grid iterations we propose solvers for integral and pseudodifferential equations on closed curves which solve the problem with an optimal convergence order $\|u_N-u\|_\lambda \leq c_{\lambda ,\mu }N^{\lambda -\mu }\|u\|_\mu$, $\lambda \leq \mu$ (Sobolev norms of periodic functions) in $\mathrm {O}(N\log N)$ arithmetical operations.References
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Additional Information
- J. Saranen
- Affiliation: University of Oulu, Department of Mathematical Sciences, 90570 Oulu Finland
- Email: jsaranen@cc.oulu.fi
- G. Vainikko
- Affiliation: Institut of Mathematics, Helsinki University of Technology, 02150 Espoo, Finland
- Email: gennadi.vainikko@hut.fi
- Received by editor(s): January 11, 1995
- Received by editor(s) in revised form: July 22, 1996
- © Copyright 1998 American Mathematical Society
- Journal: Math. Comp. 67 (1998), 1473-1491
- MSC (1991): Primary 65R20; Secondary 65N35, 45E10
- DOI: https://doi.org/10.1090/S0025-5718-98-00997-1
- MathSciNet review: 1489973