Articles citing this article

The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).

Cited article:

Asymptotic expansions for the linear PDEs with oscillatory input terms; Analytical form and error analysis

Karolina Kropielnicka and Rafał Perczyński
Computers & Mathematics with Applications 156 16 (2024)
https://doi.org/10.1016/j.camwa.2023.12.012

Gaussian quadrature rules for composite highly oscillatory integrals

Menghan Wu and Haiyong Wang
Mathematics of Computation 93 (346) 729 (2023)
https://doi.org/10.1090/mcom/3878

Fast Computation of Highly Oscillatory ODE Problems: Applications in High-Frequency Communication Circuits

Sakhi Zaman, Latif Ullah Khan, Irshad Hussain and Lucian Mihet-Popa
Symmetry 14 (1) 115 (2022)
https://doi.org/10.3390/sym14010115

The HK-Sobolev space and applications to one-dimensional boundary value problems

T. Pérez-Becerra, S. Sánchez-Perales and J.J. Oliveros-Oliveros
Journal of King Saud University - Science 32 (6) 2790 (2020)
https://doi.org/10.1016/j.jksus.2020.06.016

Asymptotic-numerical solvers for highly oscillatory second-order differential equations

Zhongli Liu, Tianhai Tian and Hongjiong Tian
Applied Numerical Mathematics 137 184 (2019)
https://doi.org/10.1016/j.apnum.2018.11.004

Efficient methods for highly oscillatory integrals with weakly singular and hypersingular kernels

Bin Li and Shuhuang Xiang
Applied Mathematics and Computation 362 124499 (2019)
https://doi.org/10.1016/j.amc.2019.06.013

Asymptotic-numerical approximations for highly oscillatory second-order differential equations by the phase function method

Renato Spigler
Journal of Mathematical Analysis and Applications 463 (1) 318 (2018)
https://doi.org/10.1016/j.jmaa.2018.03.027

Uniformly accurate multiscale time integrators for second order oscillatory differential equations with large initial data

Xiaofei Zhao
BIT Numerical Mathematics 57 (3) 649 (2017)
https://doi.org/10.1007/s10543-017-0646-0

Efficient representation and accurate evaluation of oscillatory integrals and functions

Gregory Beylkin and Lucas Monzón
Discrete and Continuous Dynamical Systems 36 (8) 4077 (2016)
https://doi.org/10.3934/dcds.2016.36.4077

Stability of a modified Peaceman–Rachford method for the paraxial Helmholtz equation on adaptive grids

Qin Sheng and Hai-wei Sun
Journal of Computational Physics 325 259 (2016)
https://doi.org/10.1016/j.jcp.2016.08.040

Numerical integration of ordinary differential equations with rapidly oscillatory factors

J.E. Bunder and A.J. Roberts
Journal of Computational and Applied Mathematics 282 54 (2015)
https://doi.org/10.1016/j.cam.2014.12.033

Bounds on asymptotic-numerical solvers for ordinary differential equations with extrinsic oscillation

Bin Wang and Guolong Li
Applied Mathematical Modelling 39 (9) 2528 (2015)
https://doi.org/10.1016/j.apm.2014.10.054

Exponential splitting for n-dimensional paraxial Helmholtz equation with high wavenumbers

Qin Sheng and Hai-Wei Sun
Computers & Mathematics with Applications 68 (10) 1341 (2014)
https://doi.org/10.1016/j.camwa.2014.09.005

Asymptotic Stability of an Eikonal Transformation Based ADI Method for the Paraxial Helmholtz Equation at High Wave Numbers

Qin Sheng and Hai-Wei Sun
Communications in Computational Physics 12 (4) 1275 (2012)
https://doi.org/10.4208/cicp.100811.090112a

The “phase function” method to solve second-order asymptotically polynomial differential equations

Renato Spigler and Marco Vianello
Numerische Mathematik 121 (3) 565 (2012)
https://doi.org/10.1007/s00211-011-0441-9

Asymptotic solvers for oscillatory systems of differential equations

M. Condon, A. Deaño and A. Iserles
SeMA Journal 53 (1) 79 (2011)
https://doi.org/10.1007/BF03322583

An exponential transformation based splitting method for fast computations of highly oscillatory solutions

Qin Sheng, Shekhar Guha and Leonel P. Gonzalez
Journal of Computational and Applied Mathematics 235 (15) 4452 (2011)
https://doi.org/10.1016/j.cam.2011.04.013

Nonintrusive and Structure Preserving Multiscale Integration of Stiff ODEs, SDEs, and Hamiltonian Systems with Hidden Slow Dynamics via Flow Averaging

Molei Tao, Houman Owhadi and Jerrold E. Marsden
Multiscale Modeling & Simulation 8 (4) 1269 (2010)
https://doi.org/10.1137/090771648

On second-order differential equations with highly oscillatory forcing terms

Marissa Condon, Alfredo Deaño and Arieh Iserles
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 466 (2118) 1809 (2010)
https://doi.org/10.1098/rspa.2009.0481

On numerical methods for highly oscillatory problems in circuit simulation

Marissa Condon, Bo Hu Li, Alfredo Deaño, et al.
COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 28 (6) 1607 (2009)
https://doi.org/10.1108/03321640910999897