The three-dimensional unconditionally stable FDTD algorithm based on Crank-Nicolson method

2006 ◽  
Author(s):  
Y. Yang ◽  
Q. Han ◽  
R.S. Chen
Keyword(s):  
Three Dimensional ◽  
Unconditionally Stable ◽  
Crank Nicolson

scholarly journals Five Ways of Reducing the Crank-Nicolson Oscillations

2002 ◽  
Vol 31 (558) ◽  
Author(s):  
Ole Østerby
Keyword(s):  
Parabolic Equations ◽  
Initial Conditions ◽  
Second Order ◽  
Unconditionally Stable ◽  
Popular Method ◽  
Jump Discontinuities ◽  
Long Time ◽  
Selection Of ◽  
Crank Nicolson

Crank-Nicolson is a popular method for solving parabolic equations because it is unconditionally stable and second order accurate. One drawback of CN is that it responds to jump discontinuities in the initial conditions with oscillations which are weakly damped and therefore may persist for a long time. We present a selection of methods to reduce the amplitude of these oscillations.

scholarly journals A B-Spline Quasi Interpolation Crank–Nicolson Scheme for Solving the Coupled Burgers Equations with the Caputo–Fabrizio Derivative

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
M. Taghipour ◽  
H. Aminikhah
Keyword(s):  
Algebraic Equations ◽  
Unconditionally Stable ◽  
B Spline ◽  
Numerical Examples ◽  
Burgers Equations ◽  
Second Derivatives ◽  
Spatial Derivatives ◽  
Nicolson Scheme ◽  
Derivatives Of ◽  
Crank Nicolson

In this paper, a Crank–Nicolson finite difference scheme based on cubic B-spline quasi-interpolation has been derived for the solution of the coupled Burgers equations with the Caputo–Fabrizio derivative. The first- and second-order spatial derivatives have been approximated by first and second derivatives of the cubic B-spline quasi-interpolation. The discrete scheme obtained in this way constitutes a system of algebraic equations associated with a bi-pentadiagonal matrix. We show that the proposed scheme is unconditionally stable. Numerical examples are provided to verify the efficiency of the method.

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