A two-step, fourth-order method with energy preserving properties

摘要: Abstract We introduce a family of fourth-order two-step methods that preserve the energy function canonical polynomial Hamiltonian systems. As is case with linear mutistep and one-leg methods, prerogative new formulae associated nonlinear systems to be solved at each step integration procedure have very same dimension underlying continuous problem. The key tools in are line integral conservative vector field (such as one defined by dynamical system) its discretization obtained aid quadrature formula. Energy conservation equivalent requirement exact, which turns out always event degree precision formula high enough. non-polynomial also discussed number test problems finally presented order compare behavior theoretical results.