Energy-preserving methods and B-series
نویسندگان
چکیده
assume H : Rn → R is an invariant or the energy of the system, and that we have f(y) = S∇H(y) with S an n× n, skew-symmetric matrix1. To derive energy-preserving numerical integration methods for these problems one can use discrete gradient techniques, [5], [7]. Such methods rely on appropriate approximations of∇H(y) and S (in the case S depends on y), and in general can not be expanded in a B-series. (i.e. they are not so called B-series methods). A B-series for the system ẏ = f(y) is a formal series in powers of the step size h and in terms
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