Multistep and Runge–Kutta convolution quadrature methods for coupled dynamical systems

We consider the efficient numerical solution of coupled dynamical systems, consisting a low dimensional nonlinear part and high linear time invariant part, e.g., stemming from spatial discretization an underlying partial differential equation. The subsystem can be eliminated in frequency domain for resulting integro-differential algebraic equations, we propose combination Runge–Kutta or multistep stepping methods with appropriate convolution quadrature to handle integral terms. are shown algebraically equivalent system thus automatically inherit corresponding stability accuracy properties. After computationally expensive pre-processing step, online simulation can, however, performed at essentially same cost as solving only subsystem. proposed method is, therefore, particularly attractive, if repeated is required.