Comparison Of The Accuracy Of The Solution Of Non-Linear Equations By Euler And Fixet Point Methods Through Numerical Simulation
Abstract
Abstract: This study aims to analyze the comparison of Euler method and FixedPoint method in solving the roots of non-linear equations numerically. 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. From the four cases of solving the tested equations, the results show that the FixedPoint method is more accurate in calculating the solution of non-linear equations compared to the Euler method, with 1 iteration on trigonometric equations. on polynomial equations the Euler method is faster than the Fixed point with 1 iteration. on exponential equations the Euler method is faster than the Fixed point with 1 iteration. In the second logarithmic equation Euler method is faster than Fixed point with 1 iteration. Therefore it can be said that the Euler method has a faster convergence rate and higher accuracy than the Fixed point method in all cases. So it can be said that Euler 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, as well as contributing to the development of more efficient numerical algorithms.
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