Many of problems in engineering and science is modeled by differential equations mathematically, therefore their solutions have an important role. Various methods have been developed for analytical or numerical solutions of differential equations. In proportion to the development of technology, the numerical solution methods are utilized widely. In particular, the main objectives in real time applications are to reach the correct solution as soon as possible with minimal processing and maximum precision. In the performed study, a simulator that contains Runge-Kutta based forty-eight methods was developed for numerical solution of differential equations. In the user friendly simulator which can be used also for educational purposes, the solution of defined differential equation under the specified initial condition with given step size or according to the number of points requested within the specified range can be obtained by the selected method. Solutions can be presented to the user both numerical (step values, computation time) and graphically; also the subject explanations about the methods/solutions can be given. Furthermore, the comparative solutions (performance analysis) can be implemented by the simulator. So, the users can realize the numerical solutions of differential equations with different methods by the simulator; the students learn the methods in this field visually with the aid of subject explanation and can implement step by step; the designers can choose the most appropriate method easily, effectively and accurately for their systems by the comparative analysis.

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SUMMARYA recursive algorithm based on the use of Gauss–Seidel iterations is introduced to adjust the parameters of a self‐tuning controller for minimum phase and a class of nonminimum phase discrete‐time systems. The proposed algorithm is called the Recursive Gauss–Seidel (RGS) algorithm and is used to update the controller parameters directly. The use of the RGS algorithm with a generalized minimum variance control law is also given for nonminimum phase systems, and a forgetting factor is used to track the time‐varying parameters. Furthermore, the overall stability of the closed‐loop system is proven by using the Lyapunov stability theory. Using computer simulations, the performance of the RGS algorithm is examined and compared with the widely used recursive least squares algorithm.Copyright © 2011 John Wiley & Sons, Ltd.

The signals/systems in nature are analog in terms of their sources. These continuous-time signals/systems need to be discretized in order to be used in digital systems (processing, storage etc.). For this purpose, different methods have been developed and continue to be developed. In the work carried out; a software tool with a user-friendly interface has been designed that performs discretization of continuous-time systems with different methods in a fast, accurate and effective manner, presents single or comparative results (parameters, responses, etc.) both numerically and graphically.

Stability is one of the most important parameters / factors in the field of system analysis and design. For this reason, stability analysis should be well learned and understood in engineering education as well as need to be performed perfectly in practice. In this study; a software tool has been developed that can perform absolute, relative and conditional stability analysis for single input single output linear systems based on the Routh-Hurwitz criterion. Stability analysis of the systems defined by the user can be performed easy, fast and efficiently-including all possible general and special conditions-step-by-step in detail with the designed software tool, and the results can be obtained both numerically and graphically with many parameters.