Asymptotic solvers for ordinary differential equations with multiple frequencies

Condon, Marissa and Deaño, Alfredo and Gao, Jing and Iserles, Arieh (2015) Asymptotic solvers for ordinary differential equations with multiple frequencies. Science China Mathematics, 58 (11). pp. 2279-2300. ISSN 1674-7283. (doi:https://doi.org/10.1007/s11425-015-5066-5) (Full text available)

Abstract

We construct asymptotic expansions for ordinary differential equations with highly oscillatory forcing terms, focusing on the case of multiple, non-commensurate frequencies. We derive an asymptotic expansion in inverse powers of the oscillatory parameter and use its truncation as an exceedingly effective means to discretize the differential equation in question. Numerical examples illustrate the effectiveness of the method.

Item Type: Article
Additional information: Full text upload complies with Journal requirements
Uncontrolled keywords: highly oscillatory problems ordinary differential equation modulated Fourier expansions multiple frequencies numerical analysis
Subjects: Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus
Q Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equations
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: Alfredo Deano-Cabrera
Date Deposited: 02 Nov 2015 11:51 UTC
Last Modified: 06 Feb 2017 16:42 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/51342 (The current URI for this page, for reference purposes)
Deaño, Alfredo: https://orcid.org/0000-0003-1704-247X
  • Depositors only (login required):

Downloads

Downloads per month over past year