Journal ArticleDOI
Asymptotic-numerical solvers for highly oscillatory second-order differential equations
TLDR
An asymptotic expansion of the solution is derived in inverse of powers of the oscillatory parameter, which develops on two time scales, a slow time t and a fast time ω t .About:
This article is published in Applied Numerical Mathematics.The article was published on 2019-03-01. It has received 3 citations till now. The article focuses on the topics: Differential equation & Initial value problem.read more
Citations
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Journal ArticleDOI
Reproducing kernel-based piecewise methods for efficiently solving oscillatory systems of second-order initial value problems
F.Z. Geng,Xinyuan Wu +1 more
Journal ArticleDOI
Asymptotic-numerical solvers for diffusion equation with time-like highly oscillatory forcing terms
TL;DR: In this paper , an asymptotic expansion for the oscillatory term of the solution of diffusion equation with time-like highly oscillatory forcing terms was derived, where each term can be computed at a lower cost.
Journal ArticleDOI
Asymptotic-numerical solvers for highly oscillatory ordinary differential equations and Hamiltonian systems
TL;DR: In this paper, the authors proposed an efficient improvement on the existing asymptotic-numerical solvers, which can solve the class of highly oscillatory ordinary differential equations.
References
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Book
Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations
TL;DR: In this article, the authors present a model for symmetric integration of non-Canonical Hamiltonian systems and a model of symmetric Hamiltonian integration with symmetric integrators.
Journal ArticleDOI
Numerical integration of ordinary differential equations based on trigonometric polynomials
TL;DR: In this article, the authors present a method for the step-by-step integration of periodic or oscillatory solutions where the frequency, or some suitable substitute, can be estimated in advance.
Journal ArticleDOI
Long-Time-Step Methods for Oscillatory Differential Equations
TL;DR: Proposed in this paper is a "mollified" impulse method having an error bound that is independent of the frequency of the fast forces that is efficient and reasonably easy to implement.
Journal ArticleDOI
Long-Time Energy Conservation of Numerical Methods for Oscillatory Differential Equations
Ernst Hairer,Christian Lubich +1 more
TL;DR: This work considers second-order differential systems where high-frequency oscillations are generated by a linear part, and presents a frequency expansion of the solution, and discusses two invariants of the system that determine the coefficients of the frequency expansion.
Journal ArticleDOI
A Gautschi-type method for oscillatory second-order differential equations
TL;DR: It is proved that the method admits second-order error bounds which are independent of the product of the step size with the frequencies, which provides new insight into the García-Archilla, Sanz-Serna, and Skeel method.