Details

Autor(en) / Beteiligte

• Huebner, O

Titel

The Newton method for solving the Theodorsen integral equation

Ist Teil von

• Journal of computational and applied mathematics, 1986-02, Vol.14 (1), p.19-30

Ort / Verlag

Amsterdam: Elsevier B.V

Erscheinungsjahr

1986

Quelle

Elsevier Journal Backfiles on ScienceDirect (DFG Nationallizenzen)

Beschreibungen/Notizen

• The Newton method for the solution of the Theodorsen integral equation in conformal mapping is studied. One step of this method consists of solving a linear integral equation, the solution of which is given explicitly as the result of a Riemann-Hilbert problem. Quadratic convergence of the Newton method is established under certain assumptions. Whereas in other methods a so-called ϵ-condition with ϵ < 1 is required to hold, our method converges also for ϵ ⩾ 1. We will also present a numerical implementation in which the result of one step of the Newton method is approximately by a vector in R 2N which can be computed with 2 N log N + O( N) multiplications. In comparison, one step of the Newton method for the discrete Theodorsen equation requires O( N 3) multiplications.