On the reliability and stability of direct explicit Runge-Kutta integrators

Document Type

Journal Article


Research India Publications

Place of Publication



School of Engineering


Originally published as: Mechee, M. S., Hussain, Z. M., & Mohammed, H. R. (2016). On the reliability and stability of direct explicit Runge-Kutta integrators. Global Journal of Pure and Applied Mathematics, 12(4), 3959-3975. Available here.


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.