COMPARISON OF THE TWO PREDICTOR-CORRECTOR METHODS FOR SOLVING SYSTEMS OF NONLINEAR EQUATIONS

Abstract

The systems of nonlinear equations play vital roles in a number of applications such as science and engineering. These systems frequently arise in many branches of computational mathematics. These are usually difficult to solve analytically, therefore a numerical method is needed. Predictor-corrector methods are used for solving systems of nonlinear equations and others such as Trapezoidal Broyden method and Trapezoidal-Simpson Broyden method are among the methods used to solve systems of nonlinear equations. This project investigated solutions of system of nonlinear equation by using Simpson-midpoint newton method and Simpsonmidpoint Broyden method, which are the two predictor-corrector methods. Newton’s method and Broyden’s methods served as a predictor and the average of Simpson and midpoint rule used as a corrector for both methods. The comparisons made among these methods were based on the number of iterations and Central processing unit (per second). The convergence to the solution was investigated by numerical examples from systems of nonlinear equations. The problems including small and large systems of nonlinear equations are solved and analyzed using tables for better elaborations. All the computations were performed using MATLAB. The results indicated that Simpson-midpoint newton method takes fewer numbers of iterations to reach the approximate solution than Simpson-midpoint Broyden and the Central processing unit of Simpson-midpoint newton method is better performance than Simpson-midpoint Broyden. Finally this study recommends for further study to solve SNLEs by using one of the two predictorcorrector methods by changing the necessary parts of the codes depending up on the size of the system of nonlinear equations.