Taylor-newton homotopy method for computing the depth of flow rate for a channel

Homotopy approximation methods (HAM) can be considered as one of the new methods belong to the general classification of the computational methods which can be used to find the numerical solution of many types of the problems in science and engineering. The general problem relates to the flow and the depth of water in open channels such as rivers and canals is a nonlinear algebraic equation which is known as continuity equation. The solution of this equation is the depth of the water. This paper represents attempt to solve the equation of depth and flow using Newton homotopy based on Taylor series. Numerical example is given to show the effectiveness of the purposed method using MATLAB language

Development of Advanced Verification and Validation Procedures and Tools for the Certification of Learning Systems in Aerospace Applications

Adaptive control technologies that incorporate learning algorithms have been proposed to enable automatic flight control and vehicle recovery, autonomous flight, and to maintain vehicle performance in the face of unknown, changing, or poorly defined operating environments. In order for adaptive control systems to be used in safety-critical aerospace applications, they must be proven to be highly safe and reliable. Rigorous methods for adaptive software verification and validation must be developed to ensure that control system software failures will not occur. Of central importance in this regard is the need to establish reliable methods that guarantee convergent learning, rapid convergence (learning) rate, and algorithm stability. This paper presents the major problems of adaptive control systems that use learning to improve performance. The paper then presents the major procedures and tools presently developed or currently being developed to enable the verification, validation, and ultimate certification of these adaptive control systems. These technologies include the application of automated program analysis methods, techniques to improve the learning process, analytical methods to verify stability, methods to automatically synthesize code, simulation and test methods, and tools to provide on-line software assurance