Numerical Simulation to Find Root Solution of Nonlinear Equation with Hybrid and Laguerre Method

Safaruddin Safaruddin, Syaharuddin Syaharuddin

Abstract


Abstract: Non-linear equations are a form of mathematical problem that is often found in various fields of science, such as engineering, physics, and computers. The solution cannot always be done analytically, so the numerical approach becomes a commonly used solution. This research discusses and compares two numerical methods, namely the Hybrid method and the Laguerre method, in numerically finding the roots of non-linear equations using Matlab software. The Hybrid method combines the advantages of two methods, such as Newton-Raphson and bisection, to improve convergence speed and stability. Meanwhile, the Laguerre method is known to be efficient in solving high degree polynomial equations. The assessment is based on three main aspects: convergence speed, stability, and computational efficiency. Simulation results on various types of functions - polynomial, exponential, trigonometric, and logarithmic-show that the Hybrid method tends to have shorter computation time in some cases, while the Laguerre method shows stable performance in most trials. This study concludes that both methods have their own advantages depending on the characteristics of the function being solved. Therefore, the results of this study can be an important reference for the selection of appropriate numerical methods in the application of solving non-linear equations effectively and accurately.

Keywords


Non-linear equation roots, Hybrid Method, Laguerre Method, Numerical Method Accuracy, Convergence Rate, Stability, Computational Speed.

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