On symmetric-conjugate composition methods in the numerical integration of differential equations

We analyze composition methods with complex coefficients exhibiting the so-called “symmetry-conjugate” pattern in their distribution. In particular, we study behavior respect to preservation of qualitative properties when projected on real axis and compare them usual left-right palindromic compositions. New schemes within this family up order 8 are proposed efficiency is tested several examples. Our analysis shows that higher-order more efficient even time step sizes relatively large.