## Abstract

The method of Muskhelishvili for solving the biharmonic equation using conformal mapping is investigated. In [R. H. Chan, T. K. DeLillo, and M. A. Horn, SIAM J. Sci. Comput., 18 (1997), pp. 1571-1582] it was shown, using the Hankel structure, that the linear system in [N. I. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Groningen, the Netherlands] is the discretization of the identity plus a compact operator, and therefore the conjugate gradient method will converge superlinearly. Estimates are given here of the superlinear convergence in the cases when the boundary curve is analytic or in a Hölder class.

Original language | English |
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Pages (from-to) | 139-147 |

Number of pages | 9 |

Journal | SIAM Journal on Scientific Computing |

Volume | 19 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1998 |

Externally published | Yes |

## Keywords

- Biharmonic equation
- Conjugate gradient method
- Hankel matrices
- Numerical conformal mapping