Numerical long-time energy conservation for the nonlinear Schrödinger equation
作者： Ludwig Gauckler
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sci-hub.se 参考文章(25)
Claudia Wulff, Marcel Oliver, Exponentially accurate Hamiltonian embeddings of symplectic A-stable Runge–Kutta methods for Hamiltonian semilinear evolution equations Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences. ,vol. 146, pp. 1265- 1301 ,(2016) , 10.1017/S0308210515000852
Christian Lubich, Ernst Hairer, Gerhard Wanner, Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations ,(2009)
David Cohen, Ernst Hairer, Christian Lubich, Conservation of energy, momentum and actions in numerical discretizations of non-linear wave equations Numerische Mathematik. ,vol. 110, pp. 113- 143 ,(2008) , 10.1007/S00211-008-0163-9
J. A. C. Weideman, B. M. Herbst, Split-step methods for the solution of the nonlinear Schro¨dinger equation SIAM Journal on Numerical Analysis. ,vol. 23, pp. 485- 507 ,(1986) , 10.1137/0723033
D. Bambusi, N.N. Nekhoroshev, A property of exponential stability in nonlinear wave equations near the fundamental linear mode Physica D: Nonlinear Phenomena. ,vol. 122, pp. 73- 104 ,(1998) , 10.1016/S0167-2789(98)00169-9
Dario Bambusi, Birkhoff Normal Form for Some Nonlinear PDEs Communications in Mathematical Physics. ,vol. 234, pp. 253- 285 ,(2003) , 10.1007/S00220-002-0774-4
Ludwig Gauckler, Christian Lubich, Splitting Integrators for Nonlinear Schrödinger Equations Over Long Times Foundations of Computational Mathematics. ,vol. 10, pp. 275- 302 ,(2010) , 10.1007/S10208-010-9063-3
B. Cano, Conserved quantities of some Hamiltonian wave equations after full discretization Numerische Mathematik. ,vol. 103, pp. 197- 223 ,(2006) , 10.1007/S00211-006-0680-3
Arnaud Debussche, Erwan Faou, Modified Energy for Split-Step Methods Applied to the Linear Schrödinger Equation SIAM Journal on Numerical Analysis. ,vol. 47, pp. 3705- 3719 ,(2009) , 10.1137/080744578
D. Bambusi, B. Grébert, Birkhoff normal form for partial differential equations with tame modulus Duke Mathematical Journal. ,vol. 135, pp. 507- 567 ,(2006) , 10.1215/S0012-7094-06-13534-2