HIGHLY OSCILLATORY DIFFUSION-TYPE EQUATIONS
HIGHLY OSCILLATORY DIFFUSION-TYPE EQUATIONS
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.
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.
参考文献29
-
1B.J. Adcock, Modified Fourier Expansions: Theory, Construction and Applications, PhD Thesis, University of Cambridge, 2010. 被引量：1
-
2B.J. Adcock and A.Iserles and S.P.N0rsett, Prom high oscillation to rapid approximation II: Expansions in Birkhoff Series, IMA J. Num. Anal., (2011). 被引量：1
-
3M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover Publications Inc., 1964. 被引量：1
-
4J.P. Boyd, Chebyshev and Fourier Spectral Methods, Springer Verlag, 1989. 被引量：1
-
5E.O. Brigham, The Fast Fourier Transform Prentice-Hall, Englewood Cliffs, NJ, 1974. 被引量：1
-
6D. Cohen and E. Hairer and C. Lubich, Modulated Fourier expansions of highly oscillatory differential equations, Found. Comp. Maths., 3 (2005), 327-450. 被引量：1
-
7D. Cohen and E. Hairer and C. Lubich, Conservation of Energy, momentum and actions in numerical discretizations of nonlinear wave equations, Numer. Math., 110 (2008), 113-143. 被引量：1
-
8D. Cohen and E. Hairer and C. Lubich, Long-time analysis of nonlinearly perturbed wave equations via modulated Fourier expansions, Arch. Ration. Mech. Anal., 187 (2008), 341-368. 被引量：1
-
9E. Faou and L. Gauckler and C. Lubich, Sobolev stability of plane wave solutions to the cubic nonlinear Schrodinger equation on a torus, in press. 被引量：1
-
10L. Gauckler and C. Lubich, Nonlinear Schrodinger equations and their spectral semi-discretizations over long times, Found. Comput. Math., 10 (2010), 275-302. 被引量：1
-
1温博.中英高中物理教材中关于电场内容的比较[J].物理通报,2013,42(5):128-129.
-
2宋尔纯.扩散型半导体压力传感器的材料研究[J].国外传感技术,1993,1(1):2-5. 被引量：1
-
3边敦明.不同问题不同处理[J].湖北教育（科学课）,2013(3):88-88.
-
4张克军.初探初中数学解决问题的方案[J].教育界（教师培训）,2013(11):112-112.
-
5娄剑虹.粘贴式扩散型固态负荷传感器的研制[J].传感器应用技术,1989,7(3):52-56.
-
6陈传熙.老问题-新课标-新解决——一个平面几何问题在两个时间段的不同处理[J].中学数学月刊,2004(12):8-11.
-
7任之光,张彦通,李学迪.模糊综合评判法在高校教学评估中的应用[J].科学技术与工程,2006,6(15):2397-2401. 被引量：20
-
8Sutthisak Phongthanapanich,Pramote Dechaumphai.Adaptive nodeless variable finite elements with flux-based formulation for thermal-structural analysis[J].Acta Mechanica Sinica,2008,24(2):181-188.
-
9徐君谊,周勇.关于数学课堂动态生成的几点思考[J].科学咨询（下旬）,2012(1):121-121.
-
10初学电脑系列讲座 教你最基础的电脑知识 了解打印机之二 衡量喷墨打印机的标准[J].电脑采购,2002,0(1):23-23.
