Un calcul numérique des différentes solutions d’un système d’équations non-linéaires. (Numerical calculus of different solutions of a system of nonlinear equations). (French) Zbl 0707.65032

Bui Doan Khanh

RAIRO, Rech. Opér. 24, No. 2, 159-166 (1990).

The task to find multiple solutions of a system of nonlinear equations is tackeled via a homotopy method. Solutions are found by integrating numerically (via a Hermite predictor-corrector) the differential equation arising from differentiating the homotopy equation, parametrized by the arc-length. The part of the method gives a good approximation to each of the zeros of the original equation. This approximation is then used as a starting point in a Newton iteration. The paper concludes with some numerical examples.

Reviewer: H.Matthies

MSC:

65H10	Numerical computation of solutions to systems of equations
65H20	Global methods, including homotopy approaches to the numerical solution of nonlinear equations

Keywords:

multiple solutions; system of nonlinear equations; homotopy method; Hermite predictor-corrector; Newton iteration; numerical examples