This paper gives an overview of adaptive discretization methods for linear second-order hyperbolic problems such as the acoustic or the elastic wave equation. The emphasis is on Galerkin-type methods for spatial as well as temporal discretization, which also include variants of the Crank-Nicolson and the Newmark finite difference schemes. The adaptive choice of space and time meshes follows the...

The finite-difference time-domain (FDTD) method based on the iterated Crank–Nicolson (ICN) scheme is extended to a frequency-dependent version. Drude model used express metal dispersion, which incorporated into formulation with trapezoidal recursive convolution technique. validity of present convolutional perfectly matched layers discussed through analysis metal-insulator-metal plasmonic wavegu...

In this paper, we investigate a practical numerical method for solving one-dimensional two-sided space-fractional diffusion equation with variable coefficients in finite domain, which is based on the classical Crank-Nicolson (CN) combined Richardson extrapolation. Second-order exact estimates time and space are obtained. The unconditional stability convergence of tested. Two examples also prese...

We present a generalization of the often-used Crank-Nicolson (CN) method of obtaining numerical solutions of the time-dependent Schrödinger equation. The generalization yields numerical solutions accurate to order (Deltax)2r-1 in space and (Deltat)2M in time for any positive integers r and M, while CN employ r=M=1. We note dramatic improvement in the attainable precision (circa ten or greater o...

In this paper, we study a numerical simulation method for the initial-boundary problem of dissipative of the generalized symmetric regularized long-wave equations with damping term. A nonlinear-implicit Crank-Nicolson finite difference scheme is constructed. The scheme is a twoleveled scheme. The error estimations, convergence, stablity and uniqueness of the solution are proven by discrete ener...

We analyze the spatially semidiscrete piecewise linear finite element method for a nonlocal parabolic equation resulting from thermistor problem. Our approach is based on the properties of the elliptic projection defined by the bilinear form associated with the variational formulation of the finite element method. We assume minimal regularity of the exact solution that yields optimal order erro...

This paper studies a central difference and quartic spline approximation based exponential time differencing Crank-Nicolson (ETD-CN) method for solving systems of one-dimensional nonlinear Schrödinger equations and twodimensional nonlinear Schrödinger equations. A local extrapolation is employed to achieve a fourth order accuracy in time. The numerical method is proven to be highly efficient an...

A comparative study of the resonant charge-transfer process of H− in front of plane-model Cu surfaces of symmetries (111) and (100) is performed using a two-dimensional Crank-Nicholson wave-packet propagation approach. Very different electron evolutions near the two surfaces are related to different structures of the respective band gaps and allow for the visualization of electronic interaction...