SOLVING NONLINEAR SYSTEM OF EQUATIONS

ABSTRACT

In thisestudy, a modified successive overrelaxation iteration method called the Newton-SOR method to solve systemsroftnonlineareequations was presented. The modifiedemethod was developed using Taylor’s series expansion and matrix decomposition. By utilizing the Gauss-Seidel principle in which new values are used immediately they are determined, the SOReiterationewas used aseaemeans ofeapproximating solutionrofetheelinear system based on Newton’s method for the composite Newton-SOR iteration in which the Newton method was the primary iteration and SOR method was secondary iteration. Three problems were considered, an algebraic nonlinear system of equations of order 3 and 4. MATLAB was used to generate the approximate solutions using the initial values with stopping criteria suggested in the literature. The basic property of the algorithm such as the convergence analysis was carried out. The computational results show that the Newton-SOR method presented in this work was found to be efficient with high certainty in both operational weight and clock time.