High-order Newton-Krylov methods to solve systems of nonlinear equations. (English) Zbl 1282.65057

Darvishi, M. T.; Shin, Byeong-Chun

J. Korean Soc. Ind. Appl. Math. 15, No. 1, 19-30 (2011).

Summary: The authors and C.-H. Kim [Appl. Math. Comput. 217, No. 7, 3190–3198 (2010; Zbl 1204.65055)] compared the Newton-Krylov method and some high-order methods to solve nonlinear systems. In this paper, they propose high-order Newton-Krylov methods combining the Newton-Krylov method with some high-order iterative methods to solve systems of nonlinear equations. They provide some numerical experiments including comparisons of CPU time and iteration numbers of the proposed high-order Newton-Krylov methods for several nonlinear systems.

MSC:

65H10

Numerical computation of solutions to systems of equations

Keywords:

high-order method; Newton-Krylov method; system of nonlinear equations; numerical experiment

Citations:

Zbl 1204.65055