An error bound is proved for a fully practical piecewise linear nite element approximation, using a backward Euler time discretization, of the Cahn-Hilliard equation with a logarithmic free energy.

In this paper, we deal with a singularly perturbed parabolic convection-diffusion problem. Shishkin mesh and hybrid third-order finite difference scheme are adopted for the spatial discretization. Uniform backward Euler used temporal Furthermore, preconditioning approach is also to ensure uniform convergence. Numerical experiments show that method first-order accuracy in time almost space.

We propose a saddle-point preconditioner for an optimization problem constrained by the time-dependent Stokes equations, discretized using backward Euler method in time. The key ingredients are inner iteration (1, 1)-block, accelerated known heat control problem, and approximation of Schur complement involving commutator argument applied to block matrix. Numerical results demonstrate efficacy r...

For Ait–Sahalia-type interest rate model with Poisson jumps, we are interested in strong convergence of a novel time-stepping method, called transformed jump-adapted backward Euler method (TJABEM). Under certain hypotheses, the considered takes values positive domain. It is shown that TJABEM can preserve domain underlying problem. Furthermore, first-order recovered respect to Lp-error criterion...

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.

We consider elliptic and parabolic variational equations and inequalities governed by integro-differential operators of order 2s ∈ (0, 2]. Our main motivation is the pricing of European or American options under Lévy processes, in particular pure jump processes or jump diffusion processes with tempered stable processes. The problem is discretized using piecewise linear finite elements in space ...

This paper presents a nonlinear solver based on the Newton-Krylov methods, where the Newton equations are solved by Krylov-subspace type approaches. We focus on the solution of unsteady systems, in which the temporal terms are discretized by the backward Euler method using finite difference. To save computational cost, an adaptive time stepping is used to minimize the number of time steps. The ...

Within a thermodynamical approach associated to the classical local state postulate, a constitutive macroscopic model, named RL model [1][2], has been built in order to predict the pseudoelastic behaviour of shape memory alloys (SMA). This behaviour occurs with a martensitic transformation. The volume fraction of martensite z is taken as internal variable and the evolution kinetics of z are der...

A general outer iteration, based upon linearization, is introduced at discrete time steps for the one-dimensional semiconductor device model. The iteration depends upon solving the semidiscrete device equations approximately, specifically, in such a way that the residual is of order ∆t in an appropriate norm. It is shown that this maintains the order of the backward Euler method. A monitoring o...