Efficient numerical approximation of a non-regular Fokker-Planck equation associated with first-passage time distributions [0.03%]
与首次通过时间分布相关的非正则Fokker-Planck方程的有效数值逼近
Udo Boehm,Sonja Cox,Gregor Gantner et al.
Udo Boehm et al.
In neuroscience, the distribution of a decision time is modelled by means of a one-dimensional Fokker-Planck equation with time-dependent boundaries and space-time-dependent drift. Efficient approximation of the solution to this equation is...
Computable upper error bounds for Krylov approximations to matrix exponentials and associated [Formula: see text] -functions [0.03%]
Krylov矩阵指数和相关函数的可计算上界误差估计式
Tobias Jawecki,Winfried Auzinger,Othmar Koch
Tobias Jawecki
An a posteriori estimate for the error of a standard Krylov approximation to the matrix exponential is derived. The estimate is based on the defect (residual) of the Krylov approximation and is proven to constitute a rigorous upper bound on...
Practical splitting methods for the adaptive integration of nonlinear evolution equations. Part I: Construction of optimized schemes and pairs of schemes [0.03%]
非线性发展方程自适应积分的实用分裂方法。第I部分：优化方案和方案对的构建
Winfried Auzinger,Harald Hofstätter,David Ketcheson et al.
Winfried Auzinger et al.
We present a number of new contributions to the topic of constructing efficient higher-order splitting methods for the numerical integration of evolution equations. Particular schemes are constructed via setup and solution of polynomial sys...
Computing scattering resonances using perfectly matched layers with frequency dependent scaling functions [0.03%]
基于频率依赖缩放函数的完美匹配层计算散射共振态
Lothar Nannen,Markus Wess
Lothar Nannen
Using perfectly matched layers for the computation of resonances in open systems typically produces artificial or spurious resonances. We analyze the dependency of these artificial resonances with respect to the discretization parameters an...
Using interval unions to solve linear systems of equations with uncertainties [0.03%]
利用区间并集求解不确定线性方程组
Tiago Montanher,Ferenc Domes,Hermann Schichl et al.
Tiago Montanher et al.
An interval union is a finite set of closed and disjoint intervals. In this paper we introduce the interval union Gauss-Seidel procedure to rigorously enclose the solution set of linear systems with uncertainties given by intervals or inter...
Darryl D Holm,Tomasz M Tyranowski
Darryl D Holm
Variational integrators are derived for structure-preserving simulation of stochastic Hamiltonian systems with a certain type of multiplicative noise arising in geometric mechanics. The derivation is based on a stochastic discrete Hamiltoni...