Composition methods in the presence of small parameters (Q1899934)

The author derives numerical methods based on Gaussian quadrature for the differential equation \(\dot x = X(x) \equiv A(x) + \varepsilon B(x)\) which is a small perturbation of the exactly solvable differential equation \(\dot x = A(x)\). For the case when the system is Hamiltonian the methods are symplectic and being tested on a simple Hamiltonian system they occur to be asymptotically more accurate than known ones.