Linearly-implicit Runge-Kutta methods based on implicit Runge-Kutta methods (Q1308558)

Linearly-implicit Runge-Kutta methods (LIRKM), based on explicit Runge- Kutta schemes, are compared with implicit Runge-Kutta methods (IRKM) which require the solution of nonlinear equations by Newton-like methods. In particular, the consistency of LIRKM is investigated and the numerical expense of IRKM and LIRKM is considered. It is shown that the implementation of IRKM as a LIRKM preserves the order of IRKM and gives iterations which are near to the Newton iterations.