We consider the two-dimensional, time-dependent Schrödinger equation discretized with the Crank-Nicolson finite difference scheme. For this difference equation we derive discrete transparent boundary conditions (DTBCs) in order to get highly accurate solutions for open boundary problems. We apply inhomogeneous DTBCs to the transient simulation of quantum waveguides with a prescribed electron in...

We analyze a Crank–Nicolson–type finite difference scheme for the Kuramoto– Sivashinsky equation in one space dimension with periodic boundary conditions. We discuss linearizations of the scheme and derive second–order error estimates.

The study of this paper is two-fold: On the one hand, we generalize the high-order local absorbing boundary conditions (LABCs) proposed in [J. Zhang, Z. Sun, X. Wu and D. Wang, Commun. Comput. Phys., 10 (2011), pp. 742–766] to compute the Schrödinger equation in the semiclassical regime on unbounded domain. We analyze the stability of the equation with LABCs and the convergence of the Crank-Nic...

In this paper, we develop a priori and a posteriori error estimates for wavelet-Taylor– Galerkin schemes introduced in Refs. 6 and 7 (particularly wavelet Taylor–Galerkin scheme based on Crank–Nicolson time stepping). We proceed in two steps. In the first step, we construct the priori estimates for the fully discrete problem. In the second step, we construct error indicators for posteriori esti...

In this work, a space-time multigrid method which uses standard coarsening in both temporal and spatial domains and combines the use of different smoothers is proposed for the solution of the heat equation in one and two space dimensions. In particular, an adaptive smoothing strategy, based on the degree of anisotropy of the discrete operator on each grid-level, is the basis of the proposed mul...

Abstract. We study the error estimates for the alternating evolution discontinuous Galerkin (AEDG) method to one dimensional linear convection-diÆusion equations. The AEDG method for general convection-diÆusion equations was introduced in [H. Liu, M. Pollack, J. Comp. Phys. 307: 574–592, 2016], where stability of the semi-discrete scheme was rigorously proved for linear problems under a CFL-lik...

We introduce an adaptive space-time multigrid method for the pricing of barrier options. In particular, we consider the numerical valuation of up-and-out options by the method of lines. We treat both the implicit Euler and Crank-Nicolson methods. We implement a space-time multigrid method in which the domain in space and time are treated simultaneously. We consider an adaptive coarsening techni...

• We discretize the 2D peridynamics equation using a time Crank-Nicolson/spatial asymptotically compatible scheme. The boundary conditions prevent. corner reflections for peridynamics. numerical stability condition is proven. aim of this paper to construct accurate absorbing (ABCs) two-dimensional motion which describes nonlocal phenomena arising in continuum mechanics based on integrodifferent...

A simulation model of the human body is developed in frequency dependent Crank Nicolson finite difference time domain (FD-CN-FDTD) method. Numerical simulation of electromagnetic wave propagation inside the human head is presented. Advantages of using time discretization beyond the Courant Friedrich-Lewy (CFL) limit in FD-CN-FDTD method are shown. Parallelization using Open Multi-Processing (Op...

Complex fuzzy sets (CFSs) have recently emerged as a potent tool for expanding the scope of to encompass wider ranges within unit disk in complex plane. This study explores numbers and introduces their application first time literature address partial differential equation that involves heat under Hukuhara differentiability. The researchers utilize an implicit finite difference scheme, namely C...