SOLVING SYSTEMS OF NONLINEAR EQUATIONS BY USING DIFFERENTIAL EVOLUTION

• Main Author: KUSMIATI , YATI
• Format: Final Project
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/19702
• Institution: Institut Teknologi Bandung

Solving systems of nonlinear equations is one of the most difficult numerical computation problems. The convergences of the classical solvers such as Newtontype <br /> <br /> <br /> methods are highly sensitive to the initial guess of the solution. However, it is not easy to select good initial solutions for most systems of nonlinear equations. To avoid it, the systems of nonlinear equations is transformed to the global optimization problem. There are some methods to solve optimization problem such as <br /> <br /> <br /> gradient based method. This method unable to avoid the local optimum and it needs function derivative. In recent years, there are several heuristic methods which have been developed to overcome this problem. These method do not guarantee to get the exact solution, but it can give the solution which is closely to the exact solution. Heuristic method is generally easy to implement, it converges faster and it doesn't need function derivative. In this final project, we propose to solve the systems of nonlinear equations which is transformed to the global maximization problem by using Differential Evolution method (Storn and Price, 1997), that is combined with Grouping Technique (Sidarto and Kania, 2012). This combining method is possible to get all the roots of systems of nonlinear equations, both real and complex in once running time.