https://doi.org/10.65770/SAMW3585
ABSTRACT
Root-finding for nonlinear equations is a fundamental problem in numerical analysis. Classical bracketing methods, such as the bisection and false position methods, exhibit strong stability but rely heavily on the selection of an initial interval that contains a root. This study proposes an integration of the Monte Carlo method and a hybrid trisection–false position method for the global solution of nonlinear equations. The Monte Carlo method is employed to identify subintervals containing roots, including multiple roots, while the hybrid trisection–false position method is utilized to accelerate convergence toward the desired solution. Numerical experiments were conducted using Python programming on several nonlinear functions with 3,000 random samples. The results demonstrate that the proposed approach can effectively detect root-containing intervals and obtain accurate root approximations with a relatively small number of iterations. Therefore, the proposed method provides an effective alternative for the global solution of nonlinear equations.
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