Abstract This work introduces a new one-step method with three intermediate points for solving stiff differential systems. These types of problems appear in different disciplines and, particular, derived from chemical reactions. In fact, the term “stiff”’ was coined by Curtiss and Hirschfelder an article on kinetics (Hirschfelder, Proc Natl Acad Sci USA 38:235–243, 1952). The techniques interpo...

We give an algorithm for efficient step size control in numerical integration of non– stiff initial value problems, based on a formula tailormade to methods where the numerical solution is compared with a solution of lower order.

A partitioned implicit-explicit orthogonal Runge-Kutta method (PIROCK) is proposed for the time integration of diffusion-advection-reaction problems with possibly severely stiff reaction terms and stiff stochastic terms. The diffusion terms are solved by the explicit second order orthogonal Chebyshev method (ROCK2), while the stiff reaction terms (solved implicitly) and the advection and noise ...

A partitioned implicit-explicit orthogonal Runge-Kutta method (PIROCK) is proposed for the time integration of diffusion-advection-reaction problems with possibly severely stiff reaction terms and stiff stochastic terms. The diffusion terms are solved by the explicit second order orthogonal Chebyshev method (ROCK2), while the stiff reaction terms (solved implicitly) and the advection and noise ...

For many systems of differential equations modeling problems in science and engineering, there are often natural splittings of the right hand side into two parts, one of which is non-stiff or mildly stiff, and the other part is stiff. Such systems can be efficiently treated by a class of implicit-explicit (IMEX) diagonally implicit multistage integration methods (DIMSIMs), where the stiff part ...