A Novel Method to Deduce a High-Order Compact Difference Scheme for the Three-Dimensional Semilinear Convection-Diffusion Equation with Variable Coefficients

2013 ◽  
Vol 63 (5) ◽  
pp. 425-455 ◽  
Author(s):  
Shuying Zhai ◽  
Xinlong Feng ◽  
Demin Liu
Keyword(s):  
Diffusion Equation ◽  
Difference Scheme ◽  
Three Dimensional ◽  
Variable Coefficients ◽  
High Order ◽  
Compact Difference Scheme ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Compact Difference ◽  
Novel Method

scholarly journals New High-Order Compact ADI Algorithms for 3D Nonlinear Time-Fractional Convection-Diffusion Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Shuying Zhai ◽  
Xinlong Feng ◽  
Zhifeng Weng
Keyword(s):  
Diffusion Equation ◽  
Time Derivative ◽  
Three Dimensional ◽  
Cost Effective ◽  
Linearization Method ◽  
High Order ◽  
Thomas Algorithm ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Alternating Direction

Numerical approximations of the three-dimensional (3D) nonlinear time-fractional convection-diffusion equation is studied, which is firstly transformed to a time-fractional diffusion equation and then is solved by linearization method combined with alternating direction implicit (ADI) method. By using fourth-order Padé approximation for spatial derivatives and classical backward differentiation method for time derivative, two new high-order compact ADI algorithms with ordersO(τmin(1+α,2−α)+h4)andO(τ2−α+h4)are presented. The resulting schemes in each ADI solution step corresponding to a tridiagonal matrix equation can be solved by the Thomas algorithm which makes the computation cost effective. Numerical experiments are shown to demonstrate the high accuracy and robustness of two new schemes.

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