Implicit approximate decoupling procedure with Crank–Nicolson scheme for bandpass symmetric rotationally geophysical problems

2021 ◽  
Author(s):  
Shihong Wu ◽  
Yunyun Dong ◽  
Lining Liu ◽  
Feng Su ◽  
Xiangguang Chen
Keyword(s):  
Nicolson Scheme ◽  
Crank Nicolson

Beam Propagation Method Based on the Iterated Crank–Nicolson Scheme for Solving Large-Scale Wave Propagation Problems

2015 ◽  
Vol 51 (3) ◽  
pp. 1-4 ◽  
Author(s):  
Dimitra A. Ketzaki ◽  
Ioannis T. Rekanos ◽  
Theodoros I. Kosmanis ◽  
Traianos V. Yioultsis
Keyword(s):  
Wave Propagation ◽  
Large Scale ◽  
Beam Propagation Method ◽  
Beam Propagation ◽  
Nicolson Scheme ◽  
Crank Nicolson

scholarly journals A Mixed Element Algorithm Based on the Modified L1 Crank–Nicolson Scheme for a Nonlinear Fourth-Order Fractional Diffusion-Wave Model

2021 ◽  
Vol 5 (4) ◽  
pp. 274
Author(s):  
Jinfeng Wang ◽  
Baoli Yin ◽  
Yang Liu ◽  
Hong Li ◽  
Zhichao Fang
Keyword(s):  
Fourth Order ◽  
Mixed Finite Element ◽  
Calculated Data ◽  
Coupled System ◽  
Wave Model ◽  
Fractional Diffusion ◽  
Second Order ◽  
Diffusion Wave ◽  
Nicolson Scheme ◽  
Crank Nicolson

In this article, a new mixed finite element (MFE) algorithm is presented and developed to find the numerical solution of a two-dimensional nonlinear fourth-order Riemann–Liouville fractional diffusion-wave equation. By introducing two auxiliary variables and using a particular technique, a new coupled system with three equations is constructed. Compared to the previous space–time high-order model, the derived system is a lower coupled equation with lower time derivatives and second-order space derivatives, which can be approximated by using many time discrete schemes. Here, the second-order Crank–Nicolson scheme with the modified L1-formula is used to approximate the time direction, while the space direction is approximated by the new MFE method. Analyses of the stability and optimal L2 error estimates are performed and the feasibility is validated by the calculated data.

scholarly journals Crank-Nicolson scheme for two-dimensional in space fractional diffusion equations with functional delay

2021 ◽  
Vol 57 ◽  
pp. 128-141
Author(s):  
M. Ibrahim ◽  
V.G. Pimenov
Keyword(s):  
Piecewise Linear ◽  
Linear Interpolation ◽  
Fractional Diffusion ◽  
Dimensional System ◽  
Two Dimensional ◽  
Piecewise Linear Interpolation ◽  
Functional Delay ◽  
General Difference ◽  
Nicolson Scheme ◽  
Crank Nicolson

A two-dimensional in space fractional diffusion equation with functional delay of a general form is considered. For this problem, the Crank-Nicolson method is constructed, based on shifted Grunwald-Letnikov formulas for approximating fractional derivatives with respect to each spatial variable and using piecewise linear interpolation of discrete history with continuation extrapolation to take into account the delay effect. The Douglas scheme is used to reduce the emerging high-dimensional system to tridiagonal systems. The residual of the method is investigated. To obtain the order of the method, we reduce the systems to constructions of the general difference scheme with heredity. A theorem on the second order of convergence of the method in time and space steps is proved. The results of numerical experiments are presented.

The Semi-Discrete Finite Element Method for the Cauchy Equation

2014 ◽  
Vol 668-669 ◽  
pp. 1130-1133
Author(s):  
Lei Hou ◽  
Xian Yan Sun ◽  
Lin Qiu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Results ◽  
Cauchy Equation ◽  
The Time Domain ◽  
Nicolson Scheme ◽  
Discrete Finite Element ◽  
Better Than ◽  
Element Method ◽  
Crank Nicolson

In this paper, we employ semi-discrete finite element method to study the convergence of the Cauchy equation. The convergent order can reach. In numerical results, the space domain is discrete by Lagrange interpolation function with 9-point biquadrate element. The time domain is discrete by two difference schemes: Euler and Crank-Nicolson scheme. Numerical results show that the convergence of Crank-Nicolson scheme is better than that of Euler scheme.

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