28 research outputs found
Stochastic B-series analysis of iterated Taylor methods
For stochastic implicit Taylor methods that use an iterative scheme to
compute their numerical solution, stochastic B--series and corresponding growth
functions are constructed. From these, convergence results based on the order
of the underlying Taylor method, the choice of the iteration method, the
predictor and the number of iterations, for It\^o and Stratonovich SDEs, and
for weak as well as strong convergence are derived. As special case, also the
application of Taylor methods to ODEs is considered. The theory is supported by
numerical experiments
Guidance on the Selection of Efficient Computational Methods for Multimedia Fate Models
Runge-Kutta Research in Trondheim
Runge-Kutta research in Trondheim began in 1970 when Syvert P. Nørsett was appointed to the NTH. Although the group has worked on various aspects of Runge-Kutta methods, we have elected, in this paper, to focus on DIRK methods, linear stability, order stars, parallel methods and continuous explicit methods
Transport av jord og næringsstoffer i overflate- og grøfteavrenning
I henhold til vannforskriften skal tilførsler av næringsstoffer til vann og vassdrag reduseres for å oppnå tilfredsstillende økologisk tilstand i vannforekomsten. Kunnskap om hvordan jordpartikler og næringsstoffer transporteres med henholdsvis overflate- og grøfteavrenning på jordbruksarealer er nødvendig for å vurdere effekter av ulike tiltak mot landbruksforurensning
An Analysis of The Order of Runge-Kutta Methods That Use an Iterative Scheme To Compute Their Internal Stage Values
We employ B-series to analyze the order of Runge-Kutta (RK) methods that use simple iteration, modified Newton iteration or full Newton iteration to compute their internal stage values. Our assumptions about the initial guess for the internal stage values cover a wide range of practical schemes. Moreover, the analytical techniques developed in this paper can be applied in many other similar contexts