Local and Global Error Estimation and Control Within Explicit Two-Step Peer Triples

Journal of Computational and Applied Mathematics, 262 (2014), 261-270
http://dx.doi.org/10.1016/j.cam.2013.07.041

This paper elaborates a global error estimation and control mechanism in explicit two-step peer methods. These recently designed methods exhibit their high efficiency even in comparison to the best explicit Runge–Kutta pairs. More precisely, we form here triples of the so-called superconvergent explicit peer schemes and show that they are cheap and able to achieve preassigned accuracy conditions in automatic mode. For comparison, we present also numerical data derived by built-in explicit Matlab ODE solvers implemented with only local error control. Especially, we point out that a scaled global error is computed and regulated in this paper in contrast to the earlier published results where the absolute values of the global error have been utilized.