A multi level linearized Crank–Nicolson scheme for Richards equation under variable flux boundary conditions

2021 ◽  
pp. 1-17
Author(s):  
Fengnan Liu ◽  
Yasuhide Fukumoto ◽  
Xiaopeng Zhao
Keyword(s):  
Boundary Conditions ◽  
Richards Equation ◽  
Flux Boundary Conditions ◽  
Multi Level ◽  
Nicolson Scheme ◽  
Variable Flux ◽  
Crank Nicolson

Scaling of the Richards Equation Under Invariant Flux Boundary Conditions

1991 ◽  
Vol 27 (9) ◽  
pp. 2181-2185 ◽  
Author(s):  
M. Kutilek ◽  
K. Zayani ◽  
R. Haverkamp ◽  
J. Y. Parlance ◽  
G. Vachaud
Keyword(s):  
Boundary Conditions ◽  
Richards Equation ◽  
Flux Boundary Conditions

Second-Order Convergence and Unconditional Stability on Crank-Nicolson Scheme for Burgers’ Equation

2013 ◽  
Vol 871 ◽  
pp. 15-20
Author(s):  
Quan Zheng ◽  
Lei Fan ◽  
Guan Ying Sun
Keyword(s):  
Boundary Conditions ◽  
Heat Equation ◽  
Burgers Equation ◽  
Second Order ◽  
Dirichlet Boundary Conditions ◽  
Second Order Convergence ◽  
Nicolson Scheme ◽  
Homogeneous Dirichlet Boundary Conditions ◽  
Robin Boundary ◽  
Crank Nicolson

In this paper, we study the numerical solution of one-dimensional Burgers equation with non-homogeneous Dirichlet boundary conditions. This nonlinear problem is converted into the linear heat equation with non-homogeneous Robin boundary conditions by Hopf-Cole transformation. The heat equation is discretized by Crank-Nicolson finite difference scheme, and the fourth-order difference schemes for the Robin conditions are combined with the Crank-Nicolson scheme at two endpoints. The proposed method is proved to be second-order convergent and unconditionally stable. The numerical example supports the theoretical results.

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