The convergence of a new symmetric iterative splitting method for non-autonomous systems

References

• Aguilera-Navarro , V. C. , Estévez , G. A. and Guardiola , R. 1990 . Variational and perturbative schemes for a spiked harmonic oscillator . J. Math. Phys. , 31 : 99 – 104 .
   Web of Science ®Google Scholar
• Bátkai , A. , Csomós , P. , Farkas , B. and Nickel , G. 2011 . Operator splitting for non-autonomous evolution equations . J. Funct. Anal. , 260 ( 7 ) : 2163 – 2190 .
   Web of Science ®Google Scholar
• Baye , D. , Goldstein , G. and Capel , P. 2003 . Fourth-order factorization of the evolution operator for time-dependent potentials . Phys. Lett. A , 317 : 337 – 342 .
   Web of Science ®Google Scholar
• Bjørhus , M. 1998 . Operator splitting for abstract Cauchy problems . IMA J. Numer. Anal. , 18 : 419 – 443 .
   Web of Science ®Google Scholar
• Blanes , S. and Moan , P. C. 2001 . Splitting methods for non-autonomous Hamiltonian equations . J. Comput. Phys. , 170 : 205 – 230 .
   Web of Science ®Google Scholar
• Blanes , S. and Moan , P. C. 2006 . Fourth- and sixth-order commutator free Magnus integrators for, linear and nonlinear dynamical systems . Appl. Numer. Math. , 56 : 1519 – 1537 .
   Web of Science ®Google Scholar
• Blanes , S. and Ponsoda , E. 2012 . Time-averaging and exponential integrators for non-homogeneous linear IVPs and BVPs . Appl. Numer. Math. , 62 ( 8 ) : 875 – 894 .
   Web of Science ®Google Scholar
• Blanes , S. , Casas , F. , Oteo , J. A. and Ros , J. 2009 . The Magnus expansion and some of its applications . Phys. Rep. , 470 : 151 – 238 .
   Web of Science ®Google Scholar
• Chin , S. A. and Anisimov , P. 2006 . Gradient symplectic algorithms for solving the radial Schrödinger equation . J. Chem. Phys. , 124
   PubMed Web of Science ®Google Scholar
• Chin , S. A. and Chen , C. R. 2002 . Gradient symplectic algorithms for solving the Schrödinger equation with time-dependent potentials . J. Chem. Phys. , 117 ( 4 ) : 1409 – 1415 .
   Web of Science ®Google Scholar
• Farago , I. 2008 . A modified iterated operator splitting method . Appl. Math. Model. , 32 ( 8 ) : 1542 – 1551 .
   Web of Science ®Google Scholar
• Farago , I. and Geiser , J. 2007 . Iterative operator-splitting methods for linear problems . Int. J. Comput. Sci. Eng. , 3 : 255 – 263 .
   Google Scholar
• Geiser , J. May 2009 . Decomposition Methods for Differential Equations: Theory and Application , May , London : CRC Press .
   Google Scholar
• Geiser , J. 2008 . Iterative operator-splitting methods with higher-order time integration methods and applications for parabolic partial differential equations . J. Comput. Appl. Math. , 217 : 227 – 242 .
   Web of Science ®Google Scholar
• Goldstein , G. and Baye , D. 2004 . Sixth-order factorization of the evolution operator for time-dependent potentials . Phys. Rev. E , 70
   Web of Science ®Google Scholar
• González , C. , Ostermann , A. and Thalhammer , M. 2006 . A second-order Magnus-type integrator for nonautonomous parabolic problems . J. Comput. Appl. Math. , 189 : 142 – 156 .
   Web of Science ®Google Scholar
• Jahnke , T. and Altıntan , D. 2004 . Efficient simulation of discrete stochastic reaction system with a splitting method . BIT Numer. Math. , 50 ( 4 ) : 797 – 822 .
   Web of Science ®Google Scholar
• Lara , L. 2005 . A numerical method for solving a system of nonautonomous linear ordinary differential equations . Appl. Math. Comput. , 170 : 86 – 94 .
   Web of Science ®Google Scholar
• Moan , C. and Niesen , J. 2008 . Convergence of the Magnus series . Found. Comput. Math. , 8 : 291 – 301 .
   Web of Science ®Google Scholar
• Vigo-Aguiar , J. and Ramos , H. 2003 . Dissipative Chebyshev exponential-fitted methods for numerical solutions of second-order differential equations . J. Comput. Appl. Math. , 158 : 187 – 211 .
   Web of Science ®Google Scholar