Comparison of the Accuracy of Solution of Nonlinear Equations by Chebyshev and Euler Methods through Numerical Simulation

Ikhwanul Muslimin, Syaharuddin Syaharuddin

Abstract


Abstract: Non-linear equations have an important role in various fields of science such as physics, biology, and especially mathematics. The complexity of the mathematical form of non-linear equations often makes it difficult to solve analytically, so numerical approaches become a widely used alternative. Numerical methods offer approximate solutions to analytical solutions with certain errors, but are still reliable for various practical purposes. This study compares the accuracy of two numerical methods, namely the Chebyshev method and the Euler method, in solving non-linear equations through numerical simulations. The Chebyshev method is used to analyze the proportion of values within a certain standard deviation from the mean, while the Euler method is known as a simple one-step method with low accuracy, but faster computation process. Simulations were performed on four types of functions: trigonometric, exponential, logarithmic, and polynomial. The simulation results show that the Euler method gives a faster convergence rate than the Chebyshev method in all cases of the functions tested, so it is considered more accurate in solving the roots of non-linear equations in the context of this study. This finding is expected to be a reference in the selection of efficient and appropriate numerical methods in solving non-linear mathematical problems.

Keywords


Non-Linear Equations, Numerical Methods, Chebyshev Method, Euler Method, Numerical Simulation, Approximate Solution, Convergence Rate.

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