A fast algorithm to solve systems of nonlinear equations - Amiri, Abdolreza; Cordero, Alicia; Darvishi, Mohammad Taghi; Torregrosa, Juan R. (Journal of computational and applied mathematics, 2019)
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 Newton–HSS 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.