Embedded Files
Here we can find some notes from the course
given at Basque Center for Applied Mathematics in February 2010
Couse 1, Generalities about dispersive equations, Fourier analysis tools, etc... PDF
Course 2, Approximation of the NSE by complex Ginzburgh Landau, PDF
Course 3, Numerical schemes with uniform dispersive properties (uniform Strichartz like estimates), PDF
Course 4, Error estimates for finite difference approximations, PDF
Course 5, Splitting methods,
Lie's method for Lipschitz nonlinearities given in the course PDF
Strang's method for the same nonlinearities PDF
A local error method presented in [5] PDF
How to obtain the global error once you know a local error estimate [4] PDF
Notes by Pauline Klein, PDF
Some bibliography
- Introduction to Nonlinear Dispersive Equations (Universitext), Felipe Linares (Author), Gustavo Ponce (Author)
- Finite Difference Schemes and Partial Differential Equations by John C. Strikwerda
- Semilinear Schrodinger Equations (Courant Lecture Notes) by Thierry Cazenave
- MR2429878 (2009d:65114) Lubich, Christian On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations. Math. Comp. 77 (2008), no. 264, 2141--2153.
- MR1799313 (2001k:65143) Jahnke, Tobias; Lubich, Christian Error bounds for exponential operator splittings. BIT 40 (2000), no. 4, 735--744
- MR1982673 (2004h:35211) Machihara, Shuji; Nakamura, Yoshihisa The inviscid limit for the complex Ginzburg-Landau equation. J. Math. Anal. Appl. 281 (2003), no. 2, 552--564
- MR2485456 (2010c:35179) Ignat, Liviu I.; Zuazua, Enrique Numerical dispersive schemes for the nonlinear Schrödinger equation. SIAM J. Numer. Anal. 47 (2009), no. 2, 1366--1390
- MR2277106 (2007h:35313) Ignat, Liviu I.; Zuazua, Enrique Dispersive properties of numerical schemes for nonlinear Schrödinger equations. Foundations of computational mathematics, Santander 2005, 181--207, London Math. Soc. Lecture Note Ser., 331, Cambridge Univ. Press, Cambridge, 2006
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