A fast algorithm to solve systems of nonlinear equations

[摘要] A new HSS-based algorithm for solving systems of nonlinear equations is presented and its semilocal convergence is proved. Spectral properties of the new method are investigated. Performance profile for the new scheme is computed and compared with HSS algorithm. Besides, by a numerical example in which a two-dimensional nonlinear convection diffusion equation is solved, we compare the new method and the Newton-HSS method. Numerical results show that the new scheme solves the problem faster than the NewtonHSS scheme in terms of CPU -time and number of iterations. Moreover, the application of the new method is found to be fast, reliable, flexible, accurate, and has small CPU time. (C) 2018 Elsevier B.V. All rights reserved.

[发布日期] 2019-07-01

[效力级别]  Proceedings Paper

[关键词] Nonlinear systems;Iterative method;Newton method;Newton-HSS method;Newton-GPSS method;Jacobian free scheme