HIGHLY OSCILLATORY DIFFUSION-TYPE EQUATIONS

作     者：Sevda Uskiiplii Altlnbasak Marissa Condon Alfredo Deano Arieh Iserles 

作者机构：Department of Applied Mathematics and Theoretical Physics Centre for Mathematical Sciences University of Cambridge Cambridge UK School of Electronic Engineering Dublin City University Dublin Ireland Department of Mathematics University Carlos III de Madrid Madrid Spain Department of Applied Mathematics and Theoretical Physics Centre for Mathematical Sciences University of Cambridge Cambridge UK 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2013年第31卷第6期

页      面：549-572页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 08[工学] 070104[理学-应用数学] 081201[工学-计算机系统结构] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：A. Deano acknowledges financial support from projects (Spanish Ministry of Science and Innovation) A. Deano acknowledges financial support from projects (Spanish Ministry of Economy and Competitivity) Research Project (FWO, Fund for Scientific Research Flanders, Belgium) 

主　　题：Diffusion-type PDEs High oscillation Asymptotic expansions Modulated Fourier expansions. 

摘      要：We explore new asymptotic-numeric solvers for partial differential equations with highly oscillatory forcing terms. Such methods represent the solution as an asymptotic series, whose terms can be evaluated by solving non-oscillatory problems and they guarantee high accuracy at a low computational cost. We consider two forms of oscillatory forcing terms, namely when the oscillation is in time or in space： each lends itself to different treatment. Numerical examples highlight the salient features of the new approach.