Based on a recent novel formulation of parametric anisotropic curve shortening flow, we analyse fully discrete numerical method this geometric evolution equation. The uses piecewise linear finite elements in space and backward Euler approximation time. We establish existence uniqueness solution, as well an unconditional stability property. Some computations confirm the theoretical results demon...

The diode clipper circuit with an embedded low-pass filter lies at the heart of both diode clipping “Distortion” and “Overdrive” or “Tube Screamer” effects pedals. An accurate simulation of this circuit requires the solution of a nonlinear ordinary differential equation (ODE). Numerical methods with stiff stability – Backward Euler, Trapezoidal Rule, and second-order Backward Difference Formula...

Schemes with the second-order approximation in time are considered for numerical solving the Cauchy problem for an evolutionary equation of first order with a self-adjoint operator. The implicit two-level scheme based on the Padé polynomial approximation is unconditionally stable. It demonstrates good asymptotic properties in time and provides an adequate evolution in time for individual harmon...

Asymptotic linear stability is studied for stochastic differential equations (SDEs) that incorporate Poisson-driven jumps and their numerical simulation using theta-method discretisations. The property is shown to have a simple explicit characterisation for the SDE, whereas for the discretisation a condition is found that is amenable to numerical evaluation. This allows us to evaluate the asymp...

In this paper, we derive error estimates of the backward Euler-Maruyama method applied to multi-valued stochastic differential equations. An important example such an equation is a gradient flow whose associated potential not continuously differentiable, but assumed be convex. We show that well-defined and convergent order at least $1/4$ with respect root-mean-square norm. Our analysis relies o...

We construct and analyze the backward Euler method for one nonlinear one-dimensional parabolic equation with nonlocal boundary condition. The main objective of this article is to investigate stability convergence difference scheme in maximum norm. For purpose, we use M-matrices theory. describe some new approach estimation error solution majorant it. Some conclusions discussion our are presented.

Abstract In this paper, we study the existence and uniqueness of random periodic solution for a stochastic differential equation with one-sided Lipschitz condition (also known as monotonicity condition) convergence its numerical approximation via backward Euler–Maruyama method. The is shown limit pull-back flows SDE discretized SDE, respectively. We establish rate strong error method order 1/2.

The numerical simulation of the dynamics of the molecular beam epitaxy (MBE) growth is considered in this article. The governing equation is a nonlinear evolutionary equation that is of linear fourth order derivative term and nonlinear second order derivative term in space. The main purpose of this work is to construct and analyze two linearized finite difference schemes for solving the MBE mod...

We address the problem of approximating numerically the solutions (Xt : t ∈ [0, T ]) of stochastic evolution equations on Hilbert spaces (h, 〈·, ·〉), with respect to Brownian motions, arising in the unraveling of backward quantum master equations. In particular, we study the computation of mean values of 〈Xt, AXt〉, where A is a linear operator. First, we introduce estimates on the behavior of X...