## Fast solvers of integral and pseudodifferential equations on closed curves

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- by J. Saranen and G. Vainikko PDF
- Math. Comp.
**67**(1998), 1473-1491 Request permission

## 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