Results 21 to 30 of about 15,801 (247)

Exponential time differencing schemes for the 3-coupled nonlinear fractional Schrödinger equation

Advances in Difference Equations, 2018
Two modified exponential time differencing schemes based on the Fourier spectral method are developed to solve the 3-coupled nonlinear fractional Schrödinger equation. We compare the stability of the schemes by plotting their stability regions. The local
Xiao Liang, Harish Bhatt
doaj   +1 more source

On the convergence of Lawson methods for semilinear stiff problems [PDF]

, 2017
Since their introduction in 1967, Lawson methods have achieved constant interest in the time discretization of evolution equations. The methods were originally devised for the numerical solution of stiff differential equations. Meanwhile, they constitute
Hochbruck, Marlis, Ostermann, Alexander
core   +3 more sources

The Magnus expansion and some of its applications [PDF]

, 2008
Approximate resolution of linear systems of differential equations with varying coefficients is a recurrent problem shared by a number of scientific and engineering areas, ranging from Quantum Mechanics to Control Theory.
Abramowitz, Agrachev, Agrachev, Aparicio, Arnold, Bailey, Baker, Baker, Baye, Baye, Belinfante, Bellman, Berry, Berry, Bialynicki-Birula, Blanes, Blanes, Blanes, Blanes, Blanes, Blanes, Blanes, Blanes, Blanes, Blanes, Blanes, Bloch, Brockett, Budd, Bullo, Burrage, Burrage, Burum, Butcher, Cady, Calvo, Campbell, Casas, Casas, Casas, Casas, Casas, Celledoni, Celledoni, Chacon, Chan, Chang, Chen, Chu, Coddington, Connes, Connes, Dahmen, Dahmen, Dahmen, Dahmen, Dattoli, Degani, Devries, Dieci, Dieci, Diele, Dixmier, Dragt, Druskin, Duleba, Duleba, Dunford, Dynkin, Dyson, D’olivo, D’Olivo, D’Olivo, Eichler, Engwerda, Erdelyi, Ernst, Evans, F. Casas, Feng, Fer, Feynman, Fliess, Friedrichs, Galindo, Gamkrelidze, Gantmacher, Garrido, Golub, Gorbatsevich, Gray, Greenberg, Gronwall, Haeberlen, Hairer, Hairer, Hale, Hausdorff, Hochbruck, Hochbruck, Hochbruck, Hochbruck, Horn, Hunter, Hyman, Ince, Ionescu, Iserles, Iserles, Iserles, Iserles, Iserles, Iserles, Iserles, Iserles, Iserles, Iserles, Iserles, Iserles, J. Ros, J.A. Oteo, Jahnke, Jahnke, Jiang, Jódar, Jódar, Kalman, Karasev, Kawski, Kenney, Khan, Klarsfeld, Klarsfeld, Klarsfeld, Klarsfeld, Klarsfeld, Klarsfeld, Kloeden, Kumar, Lam, Lefebvre, Leforestier, Leimkuhler, Levante, Lord, Lorenz, Lu, Lu, Lu, Lu, Lubich, López-Ariste, López-Ariste, Magnus, Magnus, Malham, Malham, Marcus, Marthinsen, Maruyama, Mclachlan, Mclachlan, Mielnik, Milfeld, Misawa, Moan, Moan, Moan, Moler, Moler, Moore, Munthe-Kaas, Munthe-Kaas, Munthe-Kaas, Munthe-Kaas, Munthe-Kaas, Murray, Murua, Naimark, Najfeld, Olver, Oteo, Oteo, Oteo, Park, Pechukas, Platen, Postnikov, Prato, Pryce, Reid, Reimer, Reimer, Robinson, Rosen, Rossmann, S. Blanes, Saito, Salzman, San Miguel, Sanz-Serna, Schek, Schiff, Schur, Semel, Sidje, Spirig, Stefanovich, Strichartz, Supanitsky, Suárez, Sáenz, Süli, Tal-Ezer, Tani, Thalhammer, Thirring, Tyrtyshnikov, Vandersypen, Veshtort, Viswanath, Voslamber, Watkins, Waugh, Wei, Wei, Wei, Weiss, Wilcox, Wille, Wille, Yakubovich, Zanna, Zanna, Zanna, Zettl   +235 more
core   +6 more sources

LeXInt: GPU-accelerated exponential integrators package

SoftwareX
We present an open-source CUDA-based package, for the temporal integration of differential equations, that consists of a compilation of exponential integrators where the action of the matrix exponential or the φl functions on a vector is approximated ...
Pranab J. Deka, Alexander Moriggl, Lukas Einkemmer   +2 more
doaj   +1 more source

Exponential Integrators on Graphic Processing Units

, 2013
In this paper we revisit stencil methods on GPUs in the context of exponential integrators. We further discuss boundary conditions, in the same context, and show that simple boundary conditions (for example, homogeneous Dirichlet or homogeneous Neumann ...
Einkemmer, Lukas, Ostermann, Alexander
core   +1 more source

Exponential integrators for stochastic Schrödinger equations [PDF]

Physical Review E, 2020
We present a class of exponential integrators to compute solutions of the stochastic Schr dinger equation arising from the modeling of open quantum systems. In order to be able to implement the methods within the same framework as the deterministic counterpart, we express the solution using the Kunita's representation.
Jingze Li, Xiantao Li
openaire   +3 more sources

Adaptive Exponential Integrators for MCTDHF [PDF]

, 2020
We compare exponential-type integrators for the numerical time-propagation of the equations of motion arising in the multi-configuration time-dependent Hartree-Fock method for the approximation of the high-dimensional multi-particle Schr{ }dinger equation.
Winfried Auzinger, Alexander Grosz, Harald Hofstätter, Othmar Koch   +3 more
openaire   +3 more sources

Concerning product integrals and exponentials [PDF]

Proceedings of the American Mathematical Society, 1970
Suppose S S is a linearly ordered set, N N is the set of real numbers, G G is a function from S × S S \times S to N N , and all integrals are of the subdivision-refinement type. We show that if ∫ a b
Davis, W. P., Chatfield, J. A.
openaire   +1 more source

Exponential-Krylov methods for ordinary differential equations

, 2014
This paper develops a new class of exponential-type integrators where all the matrix exponentiations are performed in a single Krylov space of low dimension.
Sandu, Adrian, Tranquilli, Paul
core   +1 more source

Probabilistic Exponential Integrators

, 2023
Probabilistic solvers provide a flexible and efficient framework for simulation, uncertainty quantification, and inference in dynamical systems. However, like standard solvers, they suffer performance penalties for certain stiff systems, where small steps are required not for reasons of numerical accuracy but for the sake of stability.
Bosch, Nathanael, Hennig, Philipp, Tronarp, Filip   +2 more
openaire   +2 more sources