A multirate time stepping strategy for stiff ordinary differential equations

Abstract

To solve ODE systems with different time scales which are localized over the components, multirate time stepping is examined. In this paper we introduce a self-adjusting multirate time stepping strategy, in which the step size for a particular component is determined by its own local temporal variation, instead of using a single step size for the whole system. We primarily consider implicit time stepping methods, suitable for stiff or mildly stiff ODEs. Numerical results with our multirate strategy are presented for several test problems. Comparisons with the corresponding single-rate schemes show that substantial gains in computational work and CPU times can be obtained. (2000): 65L05, 65L06, 65L50. AMS subject classification

Linearly implicit quantization-based integration methods for stiff ordinary differential equations

“…Multi-rate methods, such as those reported in [19], exhibit a similar performance to that of LIQSS methods. They share the principle of trying to perform larger steps in variables that don't undergo rapid changes.…”

“…Making use of the aforementioned limitations, inverter chains can be used to obtain delayed signals. We consider here a chain of m inverters according to the inverter model given in [19] that is characterized by the following equations:…”

“…We used the set of parameter values proposed in [19]: m = 500 inverters, Υ = 100 (which results in a very stiff system), U thres = 1, and U op = 5.…”

Terminal Current Interpolation for Multirate Time Integration of Hierarchical IC Models

“…Multirate time-integration methods [3,4,5] appear to be attractive for initial value problems for DAEs with latency or multirate behaviour. Latency means that parts of the circuit are constant or slowly time-varying during a certain time interval, while multirate behaviour means that some variables are slowly time-varying compared to other variables.…”

Minisymposium Multirate Time Integration for Multiscaled Systems

“…Also a hierarchical multirate approach was developed to deal with various levels of dynamics behaviour [19,20]. Parallel to this, research on reaction diffusion and on systems of hyperbolic conservation laws gave rise to study Multirate Time Integration methods for the system of ODEs that arise after semidiscretization of these PDEs [6,7,17]. Here Rosenbrock methods were the starting point and also higher order methods were considered.…”