ON HIGHLY OSCILLATORY PROBLEMS ARISING IN ELECTRONIC ENGINEERING

被引：27

作者：

Condon, Marissa ^{[1
]}

Deano, Alfredo ^{[2
]}

Iserles, Arieh ^{[2
]}

机构：

[1] Dublin City Univ, Sch Elect Engn, Dublin 9, Ireland

[2] Univ Cambridge, Dept Appl Math & Theoret Phys, Ctr Math Sci, Cambridge CB3 0WA, England

来源：

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE | 2009年 / 43卷 / 04期

基金：

爱尔兰科学基金会;

关键词：

High oscillation; quadrature; ordinary differential equations; ORDINARY DIFFERENTIAL-EQUATIONS; QUADRATURE; INTEGRALS; ERROR;

D O I：

10.1051/m2an/2009024

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider linear ordinary differential equations originating in electronic engineering, which exhibit exceedingly rapid oscillation. Moreover, the oscillation model is completely different from the familiar framework of asymptotic analysis of highly oscillatory integrals. Using a Bessel-function identity, we expand the oscillator into asymptotic series, and this allows us to extend Filon-type approach to this setting. The outcome is a time-stepping method that guarantees high accuracy regardless of the rate of oscillation.

引用

页码：785 / 804

页数：20

共 20 条

[1]

Abramowitz M., 1964, HDB MATH FUNCTIONS F, V55, DOI DOI 10.1119/1.15378

[2]

[Anonymous], 1984, Methods of Numerical Integration

[3]

Cohen D., 2006, Analysis, modeling and simulation of multiscale problems, P553, DOI 10.1007/3-540-35657-620

[4] An efficient Nonlinear circuit simulation technique [J].