Mathematical  Culture and Thought

Mathematical Culture and Thought

Document Type : Translation

Subjects

‎Abdulle‎, ‎A.‎,  ‎Engquist‎, ‎W‎. ‎E‎. ‎B.‎,   ‎Vanden-Eijnden‎, ‎E.‎, ‎The heterogeneous multiscale method‎,  Acta Numerica‎, 21   (2012)‎, ‎1--87‎.
 
 
Bader‎, ‎P.‎, ‎Iserles‎, ‎A.‎,  ‎Kropielnicka‎, ‎K.‎,  ‎Singh‎, ‎P.‎,                Effective approximation for the linear time-dependent Schr\"{o}                 dinger equation,                  Technical Report NA2012/05‎, ‎DAMTP‎, ‎University of Cambridge‎, ‎2012‎.
 
‎Condon‎, ‎M.‎, ‎Dea\~{n}o‎, ‎A.‎,  ‎Iserles‎, ‎A.‎, ‎On second order differential equations with highly oscillatory forcing ‎terms,‎ Proc‎. ‎Royal Soc‎. ‎A  ‎,  466 (2010)‎, ‎1809--1828‎.
 
‎Condon‎, ‎M.‎, ‎Dea\~{n}o‎, ‎A.‎,  ‎Iserles‎, ‎A.‎, ‎On systems of differential equations with extrinsic oscillations‎,   Discr‎. ‎\& Cont‎. ‎Dynamical Sys.                 ‎,  28  (2010)‎, ‎1345--1367‎.
 
‎Hesthaven‎,  ‎J‎. ‎S‎. ‎Gottlieb‎,  ‎S.‎,   ‎Gottlieb‎, ‎D.‎, Spectral Methods for Time-Dependent Problems,  Cambridge University Press‎, ‎Cambridge‎, ‎2007‎.
 
‎Hochbruck‎, ‎M.‎,  ‎Lubich‎, ‎C.‎, ‎On Krylov subspace approximations to the matrix exponential operator‎, SIAM J‎. ‎Numer‎. ‎Anal.                 ‎,
                34   (1997)‎, ‎1911--1925‎.
 
‎Huybrechs‎,  ‎D.‎,   ‎Olver‎,  ‎S.‎, ‎Superinterpolation in highly oscillatory quadrature‎,                Found‎. ‎Comp‎. ‎Maths                 ‎,                 12                  (2012)‎, ‎203--228‎.
 
‎Huybrechs‎,  ‎D.‎,   ‎Vandewalle‎, ‎S.‎, ‎On the evaluation of highly oscillatory integrals by analytic continuation‎,                SIAM J‎. ‎Numer‎. ‎Anal.                 ‎,                 44                  (2006)‎, ‎1026--1048‎.
 
 
Iserles‎, ‎A.‎,  ‎N\o rsett‎, ‎S‎. ‎P.‎,  ‎Efficient quadrature of highly oscillatory integrals using derivatives‎,                Proc‎. ‎Royal Soc‎. ‎A                 ‎,                 461                  (2005)‎, ‎1383--1399‎.
 
Iserles‎, ‎A.‎,  ‎N\o rsett‎, ‎S‎. ‎P.‎, ‎Quadrature methods for multivariate highly oscillatory integrals using derivatives‎,                Maths Comp.                 ‎,                 75                  (2006)‎, ‎1233--1258‎.
 
 
Jin‎, ‎S.‎,   ‎Markowich‎, ‎P.‎,   ‎Sparbe‎, ‎Ch.‎, ‎Mathematical and computational methods for semiclassical Schr\"{o}dinger equations‎,
               Acta Numerica                 ‎,                 20                  (2011)‎, ‎121--210‎.
 
  Levin‎, ‎D.‎, ‎Fast integration of rapidly oscillatory functions‎, J‎. ‎Comput‎. ‎Appl‎. ‎Math.                 ‎,                 67                  (1996)‎, ‎95--101‎.
 
Olver‎, ‎F‎. ‎W‎. ‎J.‎,                Asymptotics and Special Functions,                  A K Peters Ltd‎, ‎Wellesley‎, ‎MA‎, ‎1997‎.
 
 
Olver.‎, ‎S.‎, ‎Moment-free numerical integration of highly oscillatory functions‎,                 IMA J‎. ‎Numer‎. ‎Anal.                 ‎,                 26  (2006)‎, ‎213--227‎.
Sanz-Serna.‎, ‎J‎. ‎M.‎, ‎Modulated Fourier expansions and heterogeneous multiscale methods.‎, IMA J‎. ‎Numer‎. ‎Anal. ‎, 29   (2009)‎, ‎595--605‎.

  • Receive Date 03 June 2018
  • Publish Date 22 May 2018