Analysis of a multirate theta-method for stiff ODEs

Multirate Numerical Integration for Stiff ODEs

“…In this paper we made on overview and extended the multirate time stepping strategy introduced in [7,10,11,12]. As seen from the numerical tests, the efficiency of time integration methods can be significantly improved by using large time steps for inactive components, without sacrificing accuracy.…”

“…A multirate method based on the Rosenbrock methods, together with a self-adjusting partitioning strategy was introduced and analyzed in [7,10,11,12]. In this paper we present an overview of this method and suggest a way to improve it.…”

Stability analysis of the BDF Slowest-first multirate methods

“…The efficiency gain of the multirate schemes could be destroyed by the instability, blowing up the global errors. This problem has already been investigated in other papers like [3,4,7,8,[12][13][14]. There one considers the stability of the multirate schemes applied to a two-dimensional real linear test equation.…”

Multirate Numerical Integration for Parabolic PDEs

“…For example, in [6] it was shown that the second-order trapezoidal rule with linear interpolation can lead to a firstorder consistency for stiff problems. Another important point in connection with stiff problems is that the interpolation procedures which make explicit use of some function evaluations are inappropriate.…”