Arbitrary High-order EQUIP Methods for Stochastic Canonical Hamiltonian Systems

Explicit Canonical Methods for Hamiltonian Systems

We consider canonical partitioned Runge-Kutta methods for separable Hamiltonians H = T(ß) + Viq) and canonical Runge-Kutta-Nyström methods for Hamiltonians of the form H = ^pTM~lp + Viq) with M a diagonal matrix. We show that for explicit methods there is great simplification in their structure. Canonical methods of orders one through four are constructed. Numerical experiments indicate the sui...

High-Order Symplectic Schemes for Stochastic Hamiltonian Systems

The construction of symplectic numerical schemes for stochastic Hamiltonian systems is studied. An approach based on generating functions method is proposed to generate the stochastic symplectic integration of any desired order. In general the proposed symplectic schemes are fully implicit, and they become computationally expensive for mean square orders greater than two. However, for stochasti...

Narrowing Strategies for Arbitrary Canonical Rewrite Systems

Narrowing is a universal unification procedure for equational theories defined by a canonical term rewriting system. In its original form it is extremely inefficient. Therefore, many optimizations have been proposed during the last years. In this paper, we present the narrowing strategies for arbitrary canonical systems in a uniform framework and introduce the new narrowing strategy LSE narrowi...

High order symplectic integrators for perturbed Hamiltonian systems

Abstract. We present a class of symplectic integrators adapted for the integration of perturbed Hamiltonian systems of the form H = A + εB. We give a constructive proof that for all integer p, there exists an integrator with positive steps with a remainder of order O(τε + τ ε), where τ is the stepsize of the integrator. The analytical expressions of the leading terms of the remainders are given...

Titchmarsh-Sims-Weyl theory for complex Hamiltonian systems of arbitrary order