I propose that stiffness may be defined and quantified for nonlinear systems using Lyapunov exponents, and demonstrate the relationship that exists between stiffness and the fractal dimension of a strange attractor: that stiff chaos is thin chaos. What constitutes a stiff dynamical system? Stiffness is closely related to numerical methods [1]: the signature of stiffness in a problem is that, up...

We present new implicit-explicit (IMEX) Runge Kutta methods suitable for time dependent partial differential systems which contain stiff and non stiff terms (i.e. convection-diffusion problems, hyperbolic systems with relaxation). Here we restrict to diagonally implicit schemes and emphasize the relation with splitting schemes and asymptotic preserving schemes. Accuracy and stability properties...

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...