Higher Order Super-Twisting for Perturbed Chains of Integrators

Higher order supertwisting algorithm for perturbed chains of integrators of arbitrary order

In this paper, we present a generalization for the supertwisting algorithm for perturbed chains of integrators of arbitrary order. This Higher Order Supertwisting (HOST) controller, which extends the approach of [1], is either continuous or quasi-continuous and its design is derived from a first result obtained for pure chains of integrators, the latter relying on a geometric condition introduc...

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...

Construction of higher order symplectic integrators

For Hamiltonian systems of the form H= T(p) + V(q) a method is shown to construct explicit and time reversible symplectic integrators of higher order. For any even order there exists at least one symplectic integrator with exact coefficients. The simplest one is the 4th order integrator which agrees with one found by Forest and by Ned. For 6th and 8th orders, symplectic integrators with fewer s...

Higher Order Unitary Integrators for the Schrödinger Equation

Higher Order Energy Expansions for Some Singularly Perturbed Neumann Problems

We consider the following singularly perturbed semilinear elliptic problem: 2 u ? u + u p = 0 in ; u > 0 in and @u @ = 0 on @; where is a bounded smooth domain in R N , > 0 is a small constant and p is a sub-critical exponent. Let J u] := R (2 2 jruj 2 + 1 2 u 2 ? 1 p+1 u p+1)dx be its energy functional, where u 2 H 1 ((). Ni and Takagi ((15], 16]) proved that for a single boundary spike soluti...