A method of choice for the long-time integration of constrained Hamiltonians systems is the Rattle algorithm. It is symmetric, symplectic, and nearly preserves the Hamiltonian, but it is only of order two and thus not efficient for high accuracy requirements. In this article we prove that certain symmetric linear multistep methods have the same qualitative behavior and can achieve an arbitraril...

Stiff delay differential equations are frequently utilized in practice, but their numerical simulations difficult due to the complicated interaction between stiff and terms. At moment, only a few low-order algorithms offer acceptable convergent stable features. Exponential integrators type of efficient approach for problems that can eliminate influence stiffness on scheme by precisely dealing w...