On the Energy Consumption and Accuracy of Multithreaded Embedded Runge-Kutta Methods

The family of Runge-Kutta (RK) methods provides iterative methods for the numerical approximation of solutions of ordinary differential equations (ODEs). Embedded RK methods combine the approximation computation with a step-size control exploiting an embedded solution and a predefined tolerance value. An important aspect of the computation is the accuracy that refers to how closely the approximation solution agrees with the true solution of the ODE system. The computation of solutions with a high accuracy might have a high computational demand and a high energy consumption. This article investigates the execution time and the energy consumption for a varying number of cores and varying operational frequencies. Additionally the influence of the predefined tolerance value and the resulting numerical accuracy is considered for two different types of ODE systems with different execution behavior.