28 research outputs found
General order conditions for stochastic partitioned Runge-Kutta methods
In this paper stochastic partitioned Runge-Kutta (SPRK) methods are
considered. A general order theory for SPRK methods based on stochastic
B-series and multicolored, multishaped rooted trees is developed. The theory is
applied to prove the order of some known methods, and it is shown how the
number of order conditions can be reduced in some special cases, especially
that the conditions for preserving quadratic invariants can be used as
simplifying assumptions
B-series for SDEs with application to exponential integrators for non-autonomous semi-linear problems
In this paper a set of previous general results for the development of
B--series for a broad class of stochastic differential equations has been
collected. The applicability of these results is demonstrated by the derivation
of B--series for non-autonomous semi-linear SDEs and exponential Runge-Kutta
methods applied to this class of SDEs, which is a significant generalization of
existing theory on such methods
Composition of stochastic B-series with applications to implicit Taylor methods
In this article, we construct a representation formula for stochastic
B-series evaluated in a B-series. This formula is used to give for the first
time the order conditions of implicit Taylor methods in terms of rooted trees.
Finally, as an example we apply these order conditions to derive in a simple
manner a family of strong order 1.5 Taylor methods applicable to It\^o SDEs.Comment: slight changes to improve readability. Changes resulting from the
publishing process may not be reflected in the preprint versio
Avlastningsbehov og kilderegnskap Eidsvatnet
I rapporten finnes en sammenstilling av overvåking av Eidsvatnet og tilførselsbekker i 2015, samt en teoretisk beregning av avlastningsbehovet for fosfortilførsler gitt miljømålet. Det er beregnet et enkelt kilderegnskap av fosfor, der tilførsler er splittet opp i jordbruk, avløp og utmarksavrenning
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