Abstract. This paper focuses on two variants of the Milstein scheme, namely the split-step backward Milstein method and a newly proposed projected Milstein scheme, applied to stochastic differential equations which satisfy a global monotonicity condition. In particular, our assumptions include equations with super-linearly growing drift and diffusion coefficient functions and we show that both ...

Abstract. This paper is concerned with the numerical approximation of stochastic ordinary differential equations, which satisfy a global monotonicity condition. This condition includes several equations with super-linearly growing drift and diffusion coefficient functions such as the stochastic Ginzburg-Landau equation and the 3/2-volatility model from mathematical finance. Our analysis of the ...

We show stability in a Banach space framework of backward Euler and second order backward diierence timestepping methods for a parabolic equation with memory. The results are applied to derive maximum norm stability estimates for piecewise linear nite element approximations in a plane spatial domain, which is accomplished by a new resolvent estimate for the discrete Laplacian. Error estimates a...

This paper presents a backward Euler stabilized-based control strategy applied to a neutral point clamped (NPC) back-to-back connected five level converters. A generalized method is used to obtain the back-to-back NPC converter system model. The backward Euler stabilized-based control strategy uses one set of calculations to compute the optimum voltage vector needed to reach the references and ...

This letter presents a novel cascade ΣΔ modulator architecture that employs inter-stage resonation to increase its effective resolution compared to traditional cascades while presenting very relaxed output swing requirements and, subsequently, high robustness to non-linearities of the amplifiers. In addition, the use of loop filters based on Forward-Euler integrators, instead of Backward-Euler ...

We discuss a leading-edge model used in the computation of the run-out length of dry-flowing avalanches. The model has the form of a singular initial value problem for a scalar ordinary differential equation describing the avalanche dynamics. Existence, uniqueness and smoothness properties of the analytical solution are shown. We also prove the existence of a unique root of the solution. Moreov...

A nonlinear degenerate convection-diffusion initial boundary value problem is studied in a bounded domain. A dynamical boundary condition (containing the time derivative of a solution) is prescribed on the one part of the boundary. This models a non-perfect contact on the boundary. Existence and uniqueness of a weak solution in corresponding function spaces is proved using the backward Euler me...

Numerical approximations to the solution of a linear singularly perturbed parabolic problem are generated using a backward Euler method in time and an upwinded finite difference operator in space on a piecewise-uniform Shishkin mesh for a convectiondiffusion problem. A proof is given to show first order convergence of these numerical approximations in appropriately weighted C-norm. Numerical re...

We present a semi-implicit numerical method for micromagnetics simulations, in the presence of spin-currents. The dynamics of the magnetization are described by the Landau–Lifshitz–Gilbert equation, while the dynamics of the spin are described by a diffusion equation with discontinuous coefficients. The complexity of the method presented is comparable to that of solving the linear heat equation...

(a) Show that for the solution x(t, x0) of the IVP with initial value x0 holds: ‖x(t, x0)‖ = ‖x(t0, x0)‖ . What is the geometric interpretation? Hint: Differentiate 1/2 ‖x(t)‖ and try to formulate the derivative as a scalar product! (b) Formulate an IVP in C (i.e. for complex-valued functions) equivalent (?) to the one in R in (a). (c) Consider now the numerical approximation x∆ to the IVP, whe...