Hybrid approach for solving systems of nonlinear equations using chaos optimization and quasi-Newton method

Solving systems of nonlinear equations is one of the most difficult numerical computation problems. The convergences of the classical solvers such as Newton-type methods are highly sensitive to the initial guess of the solution. However, it is very difficult to select good initial solutions for most systems of nonlinear equations. By including the global search capabilities of chaos optimization and the high local convergence rate of quasi-Newton method, a hybrid approach for solving systems of nonlinear equations is proposed. Three systems of nonlinear equations including the “Combustion of Propane” problem are used to test our proposed approach. The results show that the hybrid approach has a high success rate and a quick convergence rate. Besides, the hybrid approach guarantees the location of solution with physical meaning, whereas the quasi-Newton method alone cannot achieve this.