Comparative Analysis of Newton Rapshon and Chebyshev Methods for Numerical Solving the Roots of Nonlinear Equations

Hendi Hidayah, Syaharuddin Syaharuddin

Abstract


Abstract: This study aims to analyze the comparison of Newton-Raphson and Chebyshev methods in numerically solving the roots of non-linear equations. The assessment criteria to be used include convergence, stability, and computational speed of each method. The equations used include trigonometric, pilinomial, exponential and logarithmic. Experiments were conducted 8 times with an error of 0.001 and using a maximum of 100 iterations. Of the four cases of solving the tested equations, the newton rapshon method is faster than the cchebyshev method with 2 iterations on trigonometric equations. on polynomial equations the chebyshev method is faster than newton rapshon with 3 iterations. on exponential equations the chebyshev method is faster than newton rapshon with 14 iterations. In the logarithmic equation both methods do not find results or errors, therefore it can be said that the chebyshev method has a faster convergence rate and higher accuracy than the Newton-Raphson method in most cases. So it can be said that Chebyshev is the best method in solving the roots of non- linear equations. These findings provide new insights in choosing the right method for numerical applications in solving the roots of non-linear equations, and contribute to the development of more efficient numerical algorithms.

Keywords


Newton Raoshon, Chebyshev, Nonlinear Equations, Numerical Methods;

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References


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