Broyden’s and Thomas’ methods for identifying singular roots in nonliner systems

Abstract

Nonlinear systems is one of the mathematical models that is commonly used in the engineering and science fields and it is quite complicated to determine the root especially when the problem is singular. This study is conducted in order to study the performance of Broyden’s and Thomas’ method, which are parts of Quasi-Newton method in solving singular nonlinear systems. By applying the algorithm of each methods, we conduct the calculation to achieve the approximate solutions. MATLAB software is used to compute and present the solutions. Some of useful test problems would describe the properties and usage of the methods. Hence, both methods that have been considered in this study give well approximate solution but Thomas’ method gives better results than Broyden’s method.