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4 papers · 2 filters
Algebraic structure of stochastic expansions and efficient simulation
Kurusch Ebrahimi-Fard, Alexander Lundervold, Simon J. A. Malham +2
We investigate the algebraic structure underlying the stochastic Taylor solution expansion for stochastic differential systems.Our motivation is to construct efficient integrators.…
On algebraic structures of numerical integration on vector spaces and manifolds
Alexander Lundervold, Hans Z. Munthe-Kaas
Numerical analysis of time-integration algorithms has been applying advanced algebraic techniques for more than fourty years. An explicit description of the group of characters in…
High-order finite volume schemes for layered atmospheric models
Dante Kalise, Ivar Lie, Eleuterio F. Toro
We present a numerical scheme for the solution of a class of atmospheric models where high horizontal resolution is required while a coarser vertical structure is allowed. The prop…
Backward error analysis and the substitution law for Lie group integrators
Alexander Lundervold, Hans Munthe-Kaas
Butcher series are combinatorial devices used in the study of numerical methods for differential equations evolving on vector spaces. More precisely, they are formal series develop…