A new family of methods involving complex coefficients for the numerical integration of differential equations is presented and analyzed. They are constructed as linear combinations of symmetric-conjugate compositions obtained from a basic time-symmetric integrator of order 2n (n $\ge$ 1). The new integrators are of order 2(n + k), k = 1, 2, ..., and preserve time-symmetry up to order 4n + 3 when applied to differential equations with real vector fields. If in addition the system is Hamiltonian and the basic scheme is symplectic, then they also preserve symplecticity up to order 4n + 3. We show that these integrators are well suited for a parallel implementation, thus improving their efficiency. Methods up to order 10 based on a 4th-order integrator are built and tested in comparison with other standard procedures to increase the order of a basic scheme.
Conjugate-symplecticity properties of Euler--Maclaurin methods and their implementation on the Infinity Computer
Università degli Studi di Bari Aldo Moro（巴里阿尔多·莫罗大学）；Università della Calabria（卡拉布里亚大学）；Lobachevsky State University of Nizhni Novgorod（下诺夫哥罗德洛巴切夫斯基州立大学）
Numerical approximation to Benjamin type equations. Generation and stability of solitary waves
University of Athens（雅典大学）；Institute of Applied & Computational Mathematics, FO.R.T.H.（应用与计算数学研究所，FO.R.T.H.）；University of Valladolid（巴利亚多利德大学）；Victoria University of Wellington（惠灵顿维多利亚大学）
