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

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