نتایج جستجو برای: crank nicolson method

تعداد نتایج: 1631428  

2006
Heyu Wang Ruo Li

There have been several recent works on developing moving mesh methods for solving phase-field equations. However, it is observed that some of these moving mesh solutions are essentially different with the solutions on very fine fixed meshes. One of the purposes of this work is to understand the reason for the differences. We carried out numerical sensitivity studies systematically in this pape...

2015
P. Loganathan P. Ganesan Gurminder Singh

The effects of exponentially varying viscosity and linearly varying thermal conductivity on unsteady MHD natural convective flow past a semi infinite vertical plate in a thermally stratified medium is studied. The variables of both viscosity and thermal conductivity are considered only a function of temperature. The governing boundary layer equations of continuity, momentum and energy have been...

2011
Bart Vorselaars Jaeup U. Kim Tanya L. Chantawansri Glenn H. Fredrickson Mark W. Matsen

An efficient numerical self-consistent field theory (SCFT) algorithm is developed for treating structured polymers on spherical surfaces. The method solves the diffusion equations of SCFT with a pseudospectral approach that combines a spherical-harmonics expansion for the angular coordinates with a modified real-space Crank–Nicolson method for the radial direction. The self-consistent field equ...

2007
Ryan G. McClarren James Paul Holloway

We present a high resolution time integration method for the spherical harmonics equations based on the L-Trap method of Duraisamy, et al. This method is equivalent to the Crank-Nicolson method in smooth regions of the solution and changes form in non-smooth regions of the solution to avoid artificial oscillations in the solution. The method is nonlinear in the sense that the time integration u...

2010
Jarmo Malinen

We study a Crank–Nicolson type time discretisation (known as Tustin’s method in engineering literature) for a conservative, infinite-dimensional linear dynamical system whose transfer function is scalar and inner. We show that this discretisation approximates the state trajectory at any given time. We first prove the result for canonical Hankel range realisations, and the general case is then o...

Journal: :SIAM J. Numerical Analysis 2014
Fanhai Zeng Fawang Liu Changpin Li Kevin Burrage Ian W. Turner Vo V. Anh

In this paper, a new alternating direction implicit Galerkin–Legendre spectral method for the two-dimensional Riesz space fractional nonlinear reaction-diffusion equation is developed. The temporal component is discretized by the Crank–Nicolson method. The detailed implementation of the method is presented. The stability and convergence analysis is strictly proven, which shows that the derived ...

Journal: :Physical review. E, Statistical, nonlinear, and soft matter physics 2013
Roman Novitski Jacob Scheuer Ben Z Steinberg

We present two unconditionally stable finite-difference time-domain (FDTD) methods for modeling the Sagnac effect in rotating optical microsensors. The methods are based on the implicit Crank-Nicolson scheme, adapted to hold in the rotating system reference frame-the rotating Crank-Nicolson (RCN) methods. The first method (RCN-2) is second order accurate in space whereas the second method (RCN-...

Journal: :Journal of Interpolation and Approximation in Scientific Computing 2017

Journal: :J. Sci. Comput. 2015
Graeme Fairweather Xuehua Yang Da Xu Haixiang Zhang

A new method is formulated and analyzed for the approximate solution of a twodimensional time-fractional diffusion-wave equation. In this method, orthogonal spline collocation is used for the spatial discretization and, for the time-stepping, a novel alternating direction implicit (ADI) method based on the Crank-Nicolson method combined with the L1-approximation of the time Caputo derivative of...

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