Use of Secant Method and New Iteration Method for Numerical Simulation in Finding Solution

Zamratul Aswad, Syaharuddin Syaharuddin

Abstract


Abstract: Numerical simulation has become a very important tool in solving complex mathematical problems, especially when analytical solutions cannot be found. In this study, the use of Secant Method and New Iteration Method as two numerical methods to find the root solutions of non-linear equations are discussed. The Secant Method is used to find the roots of non-linear functions with an iterative approach that does not require explicit derivative calculations, while the New Iteration Method is applied to accelerate the solution convergence with an adaptive update technique. Both methods are applied to the search case of non-linear equations, with the aim of testing their efficiency and accuracy in numerical simulations. The results from the simulation show that both methods can provide fast and accurate solutions in finding the root of the function, although the New Iteration method shows an advantage in terms of more stable convergence on certain problems. This research also discusses the potential applications of these two methods in various scientific and engineering applications, and demonstrates their versatility in handling various types of complex non-linear equations.

 


Keywords


Secant Method, New Iteration Method, Numerical Simulation, Non-Linear Equations, Convergence.

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