A Three-Dimensional Unconditionally-Stable FDTD Method Based on Split-Step Scheme and Crank-Nicolson Scheme

2008 ◽  
Author(s):  
Qing-Xin Chu ◽  
Yong-Dan Kong
Keyword(s):  
Fdtd Method ◽  
Three Dimensional ◽  
Unconditionally Stable ◽  
Nicolson Scheme ◽  
Crank Nicolson

scholarly journals Explicit FDTD method based on iterated Crank–Nicolson scheme

2021 ◽  
Author(s):  
Jun Shibayama ◽  
Tomomasa Nishio ◽  
Junji Yamauchi ◽  
Hisamatsu Nakano
Keyword(s):  
Fdtd Method ◽  
Nicolson Scheme ◽  
Crank Nicolson

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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