01399nam a2200169 a 4500 20260901030405.0 250101s2020 xx o 000 0 eng d Zachary J. Grant Perturbed Runge-Kutta methods for mixed precision applications arXiv 2020 text online resource In this work we consider a mixed precision approach to accelerate the implemetation of multi-stage methods. We show that Runge-Kutta methods can be designed so that certain costly intermediate computations can be performed as a lower-precision computation without adversely impacting the accuracy of the overall solution. In particular, a properly designed Runge-Kutta method will damp out the errors committed in the initial stages. This is of particular interest when we consider implicit Runge-Kutta methods. In such cases, the implicit computation of the stage values can be considerably faster if the solution can be of lower precision (or, equivalently, have a lower tolerance). We provide a general theoretical additive framework for designing mixed precision Runge-Kutta methods, and use this framework to derive order conditions for such methods. Next, we show how using this approach allows Open access — freely available to read. https://arxiv.org/pdf/2012.13055v1 Read the full paper (PDF) ERES 699 699 0 0 0 3 GEN MAIN MAIN SCICOMP 2026-09-01 0 YGE000960 2026-09-01 03:04:05 https://arxiv.org/pdf/2012.13055v1 2026-09-01 PAPER