Newton Tabanlı Kök Bulma Yöntemleri İçin Simülatör Tasarımı

Abstract

In most of the engineering problems, the calculation of the roots of the equations is required. Many methods have been developed for this purpose. However, especially to obtain the roots in real-time applications with a minimum operation in minimum time, and having high accuracy are main properties. In the performed study, a graphical user interface program that contains 42 Newton-based methods is developed. In the user friendly simulator which can be used also for educational purposes, the roots of the defined/entered equations can be calculated within the specified range with a desired precision; the convergence steps (iterations) to the root can be seen as both numerical and graphical (animated or non-animated), the descriptions of subjects related to the methods are presented. Also, the performance analyzes (the iteration number, the obtained root, the computation time) of the methods can be performed comparatively. Thus, the users can perform the root-finding operations with different methods comparatively by the simulator; the students can learn and apply the methods visually in this field; the designers can choose the most appropriate method in terms of performance easily, effectively and efficiently for their systems.