Cahn-Hilliard equationstability analysis.We prove energy stability of a standard operator-splitting method for the Cahn-Hilliard equation. We establish uniform bound of Sobolev norms of the numerical solution and convergence of the splitting approximation. This is the first energy stability result for ...
In this chapter we present a numerical technique to estimate such splitting errors on the fly and dynamically adapt the splitting time steps according to a user-defined accuracy tolerance. The method applies to the numerical solution of time-dependent stiff PDEs, illustrated here by propagating ...
In this chapter we present a numerical technique to estimate such splitting errors on the fly and dynamically adapt the splitting time steps according to a user-defined accuracy tolerance. The method applies to the numerical solution of time-dependent stiff PDEs, illustrated here by propagating ...
The most recent method in this field is the overlapping Schwarz waveform relaxation scheme, as appearing in [4]. Furthermore, in this work the operator splitting method will be considered using an implicit Euler-method for the time-discretization [17]. The main advantage in considering the ...
equations introduced by us (A. Rouhi and J. Wright, A new operator splitting method for the numerical solution of partial differential equations, Comput. Phys. Commun. 85 (1995) 18–28, and Spectral implementation of a new operator splitting method for solving partial differential equations, ...
This note provides a simple proof of a worst-case convergence rate measured by the iteration complexity for the Douglas–Rachford operator splitting method... B He,X Yuan - 《Mathematical Programming》 被引量: 269发表: 2015年 On non-ergodic convergence rate of Douglas–Rachford alternating directi...
For American options, we first apply the operator splitting method that was recently developed in [12]. In the first sub-step, we solve for an intermediate solution Vñ(x) from the FBVP: (4.4)ρV1̃(x)=LV1̃(x)+c1Lg(x)+ψ0(x),ρ[V2̃(x)+ω1V1(x)]=LV2̃(x)+c2...
Starting from a 2patomic orbital aligned along the molecular axis, we solve the three-dimensional TDSE in single-active-electron approximation with the split-operator method on a Cartesian grid with 512 points in each dimension, a grid spacing of 0.25 a.u. and a time step of 0.02 a.u. Wh...
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Gauckler, L.: Convergence of a split-step Hermite method for the Gross–Pitaevskii equation. IMA J. Numer. Anal. 31, 1082–1106 (2011) Article MathSciNet MATH Google Scholar Gubinelli, M.: Rough solutions for the periodic Korteweg-de Vries equation. Comm. Pure Appl. Anal. 11, 709–...