Convergence of Fourth Order Compact Difference Schemes for Three‐Dimensional Convection‐Diffusion Equations

2007 ◽  
Vol 45 (1) ◽  
pp. 443-455 ◽  
Author(s):  
Givi Berikelashvili ◽  
Murli M. Gupta ◽  
Manana Mirianashvili
Keyword(s):  
Fourth Order ◽  
Three Dimensional ◽  
Difference Schemes ◽  
Diffusion Equations ◽  
Convection Diffusion ◽  
Compact Difference Schemes ◽  
Compact Difference

scholarly journals Compact difference schemes for convection-diffusion equations

2021 ◽  
Vol 57 (3) ◽  
pp. 311-318
Author(s):  
B. D. Utebaev
Keyword(s):  
Difference Schemes ◽  
Numerical Calculations ◽  
Diffusion Equations ◽  
Stability And Convergence ◽  
Convection Diffusion ◽  
Compact Difference Schemes ◽  
Compact Difference

This work is devoted to the construction of compact difference schemes for convection-diffusion equations with divergent and nondivergent convective terms. Stability and convergence in the discrete norms are proved. The obtained results are generalized to multidimensional convection-diffusion equations. The test numerical calculations presented in the work are consistent with the theoretical conclusions.

scholarly journals Fourth-Order Compact Difference Schemes for the Riemann-Liouville and Riesz Derivatives

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Yuxin Zhang ◽  
Hengfei Ding ◽  
Jincai Luo
Keyword(s):  
Fourth Order ◽  
Numerical Approximation ◽  
Difference Schemes ◽  
Order Convergence ◽  
Transform Method ◽  
Numerical Examples ◽  
Compact Difference Schemes ◽  
Compact Difference ◽  
The Fourier Transform ◽  
Convergence Orders

We propose two new compact difference schemes for numerical approximation of the Riemann-Liouville and Riesz derivatives, respectively. It is shown that these formulas have fourth-order convergence order by means of the Fourier transform method. Finally, some numerical examples are implemented to testify the efficiency of the numerical schemes and confirm the convergence orders.

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