000			01399nam a2200169 a 4500
005			20260901030405.0
008			250101s2020 xx o 000 0 eng d
100	1		_aZachary J. Grant
245	1	0	_aPerturbed Runge-Kutta methods for mixed precision applications
264		1	_barXiv _c2020
336			_atext
338			_aonline resource
520			_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 allows
506	0		_aOpen access — freely available to read.
856	4	0	_uhttps://arxiv.org/pdf/2012.13055v1 _yRead the full paper (PDF)
942			_cERES
999			_c699 _d699