On the reliability and stability of direct explicit Runge-Kutta integrators
Research India Publications
Place of Publication
School of Engineering
Recently, efficient direct numerical integrators of Runge-Kuta type (called RKD and RKT methods) for solving third order ordinary differential equations (ODEs) of the form y''' = f(x,x) have been proposed. In this paper, we investigate the reliability of the RKD and RKT approaches, with focus on their stability and accuracy. We compare the stability regions of RKD and RKT methods. It is found that RKD stability region is adaptable, in the sense that its area can be controlled using a free parameter to get a more stable solution. To test the accuracy of RKD, we present some examples of this approach towards solving third-order ordinary differential equations. Simulation results show that the RKD approach, n addition to outperforming the existing RKT methods in terms of accuracy and time consumption, gives better control over stability region.