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NUMERISCHE MATHEMATIK, ISSN 0029-599X, 02/2020, Volume 144, Issue 2, pp. 357 - 373
We relate two notions of local error for integration schemes on Riemannian homogeneous spaces, and show how to derive global error estimates from such local... 
53C30 | MATHEMATICS, APPLIED | Secondary 22F30 | RUNGE-KUTTA METHODS | Primary 65L20
Journal Article
Numerische Mathematik, ISSN 0029-599X, 3/2017, Volume 135, Issue 3, pp. 833 - 873
A multiscale time integrator Fourier pseudospectral (MTI-FP) method is proposed and analyzed for solving the Klein–Gordon–Schrödinger (KGS) equations in the... 
65L05 | Mathematical Methods in Physics | 65L70 | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | Mathematics, general | 65L20 | Mathematics | Numerical and Computational Physics, Simulation
Journal Article
IMA Journal of Numerical Analysis, ISSN 0272-4979, 03/2015, Volume 35, Issue 2, pp. 698 - 721
Journal Article
Journal Article
Journal of Scientific Computing, ISSN 0885-7474, 5/2018, Volume 75, Issue 2, pp. 1040 - 1056
Explicit Runge–Kutta methods are standard tools in the numerical solution of ordinary differential equations (ODEs). Applying the method of lines to partial... 
Strong-stability preserving | 65L06 | Computational Mathematics and Numerical Analysis | Algorithms | Runge–Kutta methods | Theoretical, Mathematical and Computational Physics | Mathematical and Computational Engineering | Strong stability | 65L20 | Mathematics | 65M12
Journal Article
JOURNAL OF SCIENTIFIC COMPUTING, ISSN 0885-7474, 08/2019, Volume 80, Issue 2, pp. 784 - 807
In this paper strong stability preserving (SSP) properties of Runge-Kutta methods obtained by composing k different schemes with different step sizes are... 
65L05 | 65L06 | MATHEMATICS, APPLIED | Radius of absolute monotonicity | STEPSIZE RESTRICTIONS | Initial value problem | Strong stability preserving | ABSOLUTE MONOTONICITY | CONTRACTIVITY | SSP | NUMERICAL-SOLUTION | 65L20 | Runge-Kutta | Composition method | Monotonicity | 65M20
Journal Article
Journal of Difference Equations and Applications, ISSN 1023-6198, 03/2013, Volume 19, Issue 3, pp. 466 - 490
For stochastic differential equations (SDEs) with a superlinearly growing and globally one-sided Lipschitz continuous drift coefficient, the classical explicit... 
tamed Milstein method | one-sided Lipschitz condition | commutative noise | strong convergence | superlinearly growing coefficient | 65C20 | SCHEME | MATHEMATICS, APPLIED | 65L20 | EULER | 60H35 | STRONG-CONVERGENCE | Difference equations | Mathematical analysis | Differential equations | Exact solutions | Mathematical models | Computational efficiency | Stochasticity | Convergence
Journal Article
BIT Numerical Mathematics, ISSN 0006-3835, 03/2016, Volume 56, Issue 1, pp. 151 - 162
To access, purchase, authenticate, or subscribe to the full-text of this article, please visit this link: http://dx.doi.org/10.1007/s10543-015-0549-x In this... 
Numerical methods for stochastic differential equations | Discontinuous drift | Stochastic differential equations | Monte Carlo method | Methods | Mathematics - Probability
Journal Article
Numerical Algorithms, ISSN 1017-1398, 8/2019, Volume 81, Issue 4, pp. 1253 - 1274
We show how to compute the optimal relative backward error for the numerical solution of the Dahlquist test problem by one-step methods. This is an example of... 
65L05 | 65L04 | Numeric Computing | Backward error | Theory of Computation | Stiff IVP | Residual | Algorithms | Algebra | Numerical Analysis | Optimal control | Computer Science | 65L20 | 49M05 | NUMERICAL-METHODS | MATHEMATICS, APPLIED | DEFECT CONTROL | TOLERANCE PROPORTIONALITY | ERROR-CONTROL | Analysis
Journal Article
Numerical Algorithms, ISSN 1017-1398, 8/2019, Volume 81, Issue 4, pp. 1547 - 1571
Many physical phenomena contain different scales. These phenomena can be modeled using partial differential equations (PDEs). Often, these PDEs can be split... 
65D30 | 65L05 | Multirate schemes | Algorithms | Algebra | Numerical Analysis | Computer Science | Numeric Computing | 65L20 | Theory of Computation | Numerical method | Time integration | MATHEMATICS, APPLIED | Analysis | Methods | Differential equations
Journal Article
Journal of Numerical Mathematics, ISSN 1570-2820, 03/2019, Volume 27, Issue 1, pp. 23 - 36
In engineering, it is a common desire to couple existing simulation tools together into one big system by passing information from subsystems as parameters... 
coupled problems | 65L06 | extrapolation of signals | convergence | 65L20 | 65G99 | balance correction | 65Y05 | co-simulation | stability | MATHEMATICS | MATHEMATICS, APPLIED | DYNAMIC ITERATION | Data exchange | Simulation | Convergence | Subsystems
Journal Article
BIT Numerical Mathematics, ISSN 0006-3835, 3/2014, Volume 54, Issue 1, pp. 171 - 188
The dynamical low-rank approximation of time-dependent matrices is a low-rank factorization updating technique. It leads to differential equations for factors... 
65L05 | Computational Mathematics and Numerical Analysis | Low-rank approximation | 15A23 | 65F30 | Numeric Computing | Matrix differential equations | Mathematics, general | 65L20 | Mathematics | Time-dependent matrices | Numerical integrator | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | Projectors | Rankings | Algorithms | Mathematical optimization | Analysis
Journal Article
Statistics and Computing, ISSN 0960-3174, 11/2019, Volume 29, Issue 6, pp. 1265 - 1283
Journal Article
Numerical Algorithms, ISSN 1017-1398, 02/2019, Volume 80, Issue 2, pp. 469 - 483
This paper concerns the discrete time waveform relaxation (DWR) methods for ordinary differential equations (ODEs). We present a general algorithm of... 
Discrete time waveform relaxation methods | Interpolation polynomial | Convergence | 65L05 | 65L06 | MATHEMATICS, APPLIED | 65L20 | SYSTEMS | Methods | Algorithms | Differential equations
Journal Article
Numerische Mathematik, ISSN 0029-599X, 4/2018, Volume 138, Issue 4, pp. 839 - 867
Journal Article
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