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8 papers · 2 filters
Rooted Tree Analysis for Order Conditions of Stochastic Runge-Kutta Methods for the Weak Approximation of Stochastic Differential Equations
Andreas Rößler
A general class of stochastic Runge-Kutta methods for the weak approximation of Itô and Stratonovich stochastic differential equations with a multi-dimensional Wiener process is in…
Numerical identification of a nonlinear diffusion law via regularization in Hilbert scales
Herbert Egger, Jan-Frederik Pietschmann, Matthias Schlottbom
We consider the reconstruction of a diffusion coefficient in a quasilinear elliptic problem from a single measurement of overspecified Neumann and Dirichlet data. The uniqueness fo…
Non-dissipative space-time -discontinuous Galerkin method for the time-dependent Maxwell Equations
Martin Lilienthal, Sascha M. Schnepp, Thomas Weiland
A finite element method for the solution of the time-dependent Maxwell equations in mixed form is presented. The method allows for local -refinement in space and in time. To th…
Families of efficient second order Runge-Kutta methods for the weak approximation of Itô stochastic differential equations
Kristian Debrabant, Andreas Rößler
Recently, a new class of second order Runge-Kutta methods for Itô stochastic differential equations with a multidimensional Wiener process was introduced by Rößler. In contrast to…
Classification of Stochastic Runge-Kutta Methods for the Weak Approximation of Stochastic Differential Equations
Kristian Debrabant, Andreas Rößler
In the present paper, a class of stochastic Runge-Kutta methods containing the second order stochastic Runge-Kutta scheme due to E. Platen for the weak approximation of Itô stochas…
Continuous Weak Approximation for Stochastic Differential Equations
Kristian Debrabant, Andreas Rößler
A convergence theorem for the continuous weak approximation of the solution of stochastic differential equations by general one step methods is proved, which is an extension of a t…