Asymptotic solvers for ordinary differential equations with multiple frequencies  

作　　者：CONDON Marissa DEAO Alfredo GAO Jing ISERLES Arieh 

机构地区：[1]School of Electronic Engineering,Dublin City University [2]Departmento de Matematicas,Universidad Carlos III de Madrid [3]School of Mathematics and Statistics,Xi'an Jiaotong University [4]DAMTP,Centre for Mathematical Sciences,University of Cambridge

出　　处：《Science China Mathematics》2015年第11期2279-2300,共22页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11201370 and 11371287);Projects of International Cooperation and Exchanges NSFC-RS(Grant No.1141101162);the Natural Science Basic Research Plan in Shaanxi Province of China(Grant No.2014JQ2-1006);the Fundamental Research Funds for the Central Universities

摘　　要：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.We construct asymptotic expansions for ordinary differential equations with highly oscillatory forc- ing 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.

关 键 词：highly oscillatory problems ordinary differential equation modulated Fourier expansions multiple frequencies numerical analysis 

分 类 号：O175.1[理学—数学] O322[理学—基础数学]