01353nam a2200145 a 450000500170000000800400001710000210005724500670007826400160014533600090016133800200017052009050019050600460109585600660114120260901030405.0250101s2020    xx     o     000 0 eng d1 aZachary J. Grant10aPerturbed Runge-Kutta methods for mixed precision applications 1barXivc2020  atext  aonline resource  aIn 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 allows0 aOpen access — freely available to read.40uhttps://arxiv.org/pdf/2012.13055v1yRead the full paper (PDF)