Structure-Preserving Algorithms for Oscillatory Differential Equations

Structure-Preserving Algorithms for Oscillatory Differential Equations describes a large number of highly effective and efficient structure-preserving algorithms for second-order oscillatory differential equations by using theoretical analysis and numerical validation. Structure-preserving algorithms for differential equations, especially for oscillatory differential equations, play an important role in the accurate simulation of oscillatory problems in applied sciences and engineering. The book discusses novel advances in the ARKN, ERKN, two-step ERKN, Falkner-type and energy-preserving methods, etc. for oscillatory differential equations.The work is intended for scientists, engineers, teachers and students who are interested in structure-preserving algorithms for differential equations. Xinyuan Wu is a professor at Nanjing University; Xiong You is an associate professor at Nanjing Agricultural University; Bin Wang is a joint Ph.D student of Nanjing University and University of Cambridge.

[1]  Bin Wang,et al.  Multidimensional adapted Runge-Kutta-Nyström methods for oscillatory systems , 2010, Comput. Phys. Commun..

[2]  Jianlin Xia,et al.  Order conditions for ARKN methods solving oscillatory systems , 2009, Comput. Phys. Commun..

[3]  Pablo Martín,et al.  A new family of Runge–Kutta type methods for the numerical integration of perturbed oscillators , 1999, Numerische Mathematik.

[4]  J. M. Franco,et al.  High-order P-stable multistep methods , 1990 .

[5]  J. M. Franco Runge–Kutta–Nyström methods adapted to the numerical integration of perturbed oscillators , 2002 .

[6]  J. M. Franco A 5(3) pair of explicit ARKN methods for the numerical integration of perturbed oscillators , 2003 .

[7]  Ben P. Sommeijer,et al.  Explicit Runge-Kutta (-Nyström) methods with reduced phase errors for computing oscillating solutions , 1987 .

[8]  Xinyuan Wu,et al.  A new pair of explicit ARKN methods for the numerical integration of general perturbed oscillators , 2007 .

[9]  Ben P. Sommeijer,et al.  Diagonally implicit Runge-Kutta-Nystrm methods for oscillatory problems , 1989 .

[10]  J. M. Sanz-Serna,et al.  Numerical Hamiltonian Problems , 1994 .

[11]  Wei Shi,et al.  On symplectic and symmetric ARKN methods , 2012, Comput. Phys. Commun..

[12]  Ernst Hairer,et al.  Long-Time Energy Conservation of Numerical Methods for Oscillatory Differential Equations , 2000, SIAM J. Numer. Anal..

[13]  Xinyuan Wu,et al.  A note on stability of multidimensional adapted Runge–Kutta–Nyström methods for oscillatory systems☆ , 2012 .

[14]  J. M. Franco New methods for oscillatory systems based on ARKN methods , 2006 .

[15]  Xinyuan Wu,et al.  Note on derivation of order conditions for ARKN methods for perturbed oscillators , 2009, Comput. Phys. Commun..

[16]  E. Hairer,et al.  Geometric Numerical Integration: Structure Preserving Algorithms for Ordinary Differential Equations , 2004 .