High-order unraveling of master equations for dissipative evolution

Quantum dissipative master equations: Some exact results

High-order splitting schemes for semilinear evolution equations

We first derive necessary and sufficient stiff order conditions, up to order four, for exponential splitting schemes applied to semilinear evolution equations. The main idea is to identify the local splitting error as a sum of quadrature errors. The order conditions of the quadrature rules then yield the stiff order conditions in an explicit fashion, similarly to that of Runge–Kutta schemes. Fu...

Asymptotic behavior of second-order dissipative evolution equations combining potential with non-potential effects

In the setting of a real Hilbert space H, we investigate the asymptotic behavior, as time t goes to infinity, of trajectories of second-order evolution equations ü(t) + γu̇(t) +∇φ(u(t)) +A(u(t)) = 0, where ∇φ is the gradient operator of a convex differentiable potential function φ : H → IR, A : H → H is a maximal monotone operator which is assumed to be λ-cocoercive, and γ > 0 is a damping param...

Nonlinear Stability for Dissipative Nonlinear Evolution Equations with Ellipticity

We study the Cauchy problem for a set of nonlinear evolution equations, which has been proposed for the investigation of nonlinear interaction between ellipticity and dissipation. The zero equilibrium is linearly stable for coeecients within certain range. We further establish the global existence, nonlinear stability and optimal decay rate of the solution for coeecients within the same range, ...

High order quadrature based iterative method for approximating the solution of nonlinear equations

In this paper, weight function and composition technique is utilized to speeds up the convergence order and increase the efficiency of an existing quadrature based iterative method. This results in the proposition of its improved form from a two-point quadrature based method of convergence order ρ = 3 with efficiency index EI = 1:3161 to a three-point method of convergence order ρ = 8 with EI =...