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SIAM Journal on Numerical Analysis, ISSN 0036-1429, 2019, Volume 57, Issue 2, pp. 925 - 944
In the analysis of highly oscillatory evolution problems, it is commonly assumed that a single frequency is present and that it is either constant or, at... 
Uniform accuracy | Highly oscillatory problems | Time-dependent vanishing frequency | Asymptotic expansion | time-dependent vanishing frequency | MATHEMATICS, APPLIED | uniform accuracy | NUMERICAL SCHEMES | FORMAL SERIES | highly oscillatory problems | asymptotic expansion | Numerical Analysis | Mathematics
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 07/2017, Volume 318, pp. 266 - 278
For the numerical integration of highly oscillatory problems, revised trigonometrically fitted two-step hybrid methods (RTFTSH) with equation dependent... 
Highly oscillatory problems | Two-step hybrid method | Equation dependent coefficient | Phase-lag | ORBITAL PROBLEMS | MATHEMATICS, APPLIED | RUNGE-KUTTA METHODS | INITIAL-VALUE-PROBLEMS | SCHRODINGER-EQUATION | ORDER | NUMERICAL-SOLUTION | MULTISTEP METHODS | INTEGRATION | NYSTROM METHODS | CONSTRUCTION
Journal Article
Discrete and Continuous Dynamical Systems - Series B, ISSN 1531-3492, 06/2018, Volume 23, Issue 4, pp. 1819 - 1833
Renormalization group method in the singular perturbation theory, originally introduced by Chen et al, has been proven to be very practicable in a large number... 
KBM condition | Highly oscillatory problems | Bryuno-Diophantine condition | Renormalization group method | MATHEMATICS, APPLIED | DIFFERENTIAL-EQUATIONS | highly oscillatory problems
Journal Article
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, ISSN 2070-0733, 10/2019, Volume 11, Issue 5, pp. 1114 - 1135
In this paper, we propose trigonometric polynomial reconstructions based on one five-point stencil and two two-point stencils, instead of algebraic polynomial... 
MATHEMATICS, APPLIED | EFFICIENT IMPLEMENTATION | ALGORITHM | highly oscillatory problem | ESSENTIALLY NONOSCILLATORY SCHEMES | DISCONTINUOUS GALERKIN METHOD | HIGH-ORDER | ENO SCHEMES | ACCURACY | INTERPOLATION | MECHANICS | hyperbolic conservation laws | WENO scheme | SYSTEMS | LIMITERS | Trigonometric polynomial reconstruction
Journal Article
Multiscale Modeling and Simulation, ISSN 1540-3459, 2009, Volume 7, Issue 4, pp. 1779 - 1794
Journal Article
Applied Numerical Mathematics, ISSN 0168-9274, 11/2019
Journal Article
Mathematical Modelling and Numerical Analysis, ISSN 0764-583X, 2015, Volume 49, Issue 3, p. 695
This paper is concerned with the numerical solution of nonlinear Hamiltonian highly oscillatory systems of second-order differential equations of a special... 
adiabatic invariants | Naturvetenskap | Computational Mathematics | multiple time scales | Mathematics | Natural Sciences | Beräkningsmatematik | Matematik | Highly oscillatory differential equations | modulated Fourier expansions | Fermi–Pasta–Ulam problem | high order numerical schemes
Journal Article
IMA JOURNAL OF NUMERICAL ANALYSIS, ISSN 0272-4979, 07/2019, Volume 39, Issue 3, pp. 1110 - 1133
We propose and analyse a heterogeneous multiscale method for the efficient integration of constant-delay differential equations subject to fast periodic... 
MATHEMATICS, APPLIED | delay differential equations | INTEGRATION | HETEROGENEOUS MULTISCALE METHODS | SYSTEMS | stroboscopic averaging | FORMAL SERIES | highly oscillatory problems
Journal Article
Computational Methods in Applied Mathematics, ISSN 1609-4840, 10/2019, Volume 19, Issue 4, pp. 723 - 748
We devise a Hybrid High-Order (HHO) method for highly oscillatory elliptic problems that is capable of handling general meshes. The method hinges on discrete... 
Highly Oscillatory Problems | General Meshes | 65N08 | Multiscale Methods | HHO Methods | 65N30 | 76R50 | SPACE | MATHEMATICS, APPLIED | DISCONTINUOUS GALERKIN METHODS | CONVERGENCE | HYBRIDIZATION | DIFFUSION | MSFEM | FINITE-ELEMENT-METHOD | Mathematics - Numerical Analysis
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 06/2013, Volume 243, pp. 210 - 223
Journal Article
Communications in Computational Physics, ISSN 1815-2406, 11/2010, Volume 8, Issue 5, pp. 1242 - 1263
In this paper, we use trigonometric polynomial reconstruction, instead of algebraic polynomial reconstruction, as building blocks for the weighted essentially... 
Finite difference scheme | Hyperbolic conservation laws | Highly oscillatory problem | TWENO scheme | INTERPOLATION | EFFICIENT IMPLEMENTATION | GAS-DYNAMICS | hyperbolic conservation laws | ALGORITHM | highly oscillatory problem | NEWTON | PHYSICS, MATHEMATICAL | finite difference scheme
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 09/2013, Volume 248, pp. 287 - 308
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 07/2015, Volume 282, pp. 54 - 70
We present a methodology for numerically integrating ordinary differential equations containing rapidly oscillatory terms. This challenge is distinct from that... 
Ordinary differential equations | Highly oscillatory problems | Multiscale methods | MATHEMATICS, APPLIED | APPROXIMATION | DYNAMICS | SYSTEMS | Differential equations
Journal Article
Advances in Engineering Software, ISSN 0965-9978, 2010, Volume 41, Issue 10, pp. 1200 - 1210
This article creates a new method for the numerical integration of forced and damped oscillators, and their computational implementation. It also provides a... 
Numerical solutions of ODE’s | φ-functions series | Highly oscillatory problems | Stiff problems | Series methods | Perturbed oscillators | Numerical solutions of ODE's | functions series
Journal Article
ADVANCES IN ENGINEERING SOFTWARE, ISSN 0965-9978, 10/2010, Volume 41, Issue 10-11, pp. 1200 - 1210
This article creates a new method for the numerical integration of forced and damped oscillators, and their computational implementation. It also provides a... 
POLYNOMIALS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | Numerical solutions of ODE's | Highly oscillatory problems | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Stiff problems | phi-functions series | MULTISTEP NUMERICAL-METHODS | Series methods | Perturbed oscillators | ORDINARY DIFFERENTIAL-EQUATIONS
Journal Article
Applied Numerical Mathematics, ISSN 0168-9274, 03/2019, Volume 137, pp. 184 - 202
In this paper, we propose an approach of combination of asymptotic and numerical techniques to solve highly oscillatory second-order initial value problems. An... 
Second-order ordinary differential equation | Highly oscillatory problem | Asymptotic expansion | Multiple time scales | Modulated Fourier expansion | MATHEMATICS, APPLIED | MODULATED FOURIER EXPANSIONS
Journal Article
Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 09/2016, Volume 36, Issue 9, pp. 4813 - 4827
The paper is concerned with the discretization and solution of DAEs of index 1 and subject to a highly oscillatory forcing term. Separate asymptotic expansions... 
Oscillatory frequency | Highly oscillatory problems | Numerical analysis | Modulated Fourier expansions | Differential algebraic equations | MATHEMATICS | MATHEMATICS, APPLIED | DIFFERENTIAL-ALGEBRAIC EQUATIONS | numerical analysis | modulated Fourier expansions | differential algebraic equations | oscillatory frequency
Journal Article
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