The oldest of all the shaft specifications is flex. Once the production problems had been overcome which enabled steel shafts to become a reality, early steel shaft manufacturers began to experiment with producing shafts, which possessed different amounts of resistance to bending. Through the 70 years of shaft design that have followed the introduction of the steel shaft, companies have produce...

Currently there are two general ways to solve stiff differential equations numerically. The first approach is based on implicit methods and the second uses explicit stabilized Runge–Kutta methods, also known as Chebyshev methods. Implicit methods are great for very stiff problems of not very large dimension, while stabilized explicit methods are efficient for very big systems of not very large ...

-Three methods for numerical transient analysis of Markov chains, the modified Jensen's method (Jensen's method with steady-state detection of the underlying DTMC and computation of Poisson probabilities using the method of Fox and Glynn [1]), a third-order L-stable implicit Runge-Kutta method, and a second-order L-stable method, TR-BDF2, are compared. These methods are evaluated on the basis o...

The stiffness in some systems of nonlinear differential equations is shown to be characterized by single stiff equations of the form y' = g'(x) + \\y g(x)\. The stability and accuracy of numerical approximations to the solution v = g(x), obtained using implicit one-step integration methods, are studied. An S-stability property is introduced for this problem, generalizing the concept of /4-stabi...

The importance of delay differential equations (DDEs), in modelling mathematical biological, engineering and physical problems, has motivated searchers to provide efficient numerical methods for solving such important type of differential equations. Most of these types of differential models are stiff, and suitable numerical methods must be introduced to simulate the solutions. In this paper, w...