A compact finite difference method for a class of time fractional convection-diffusion-wave equations with variable coefficients

2015 ◽  
Vol 70 (3) ◽  
pp. 625-651 ◽  
Author(s):  
Yuan-Ming Wang
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Wave Equations ◽  
Variable Coefficients ◽  
Diffusion Wave ◽  
Compact Finite Difference ◽  
Convection Diffusion ◽  
Compact Finite Difference Method

scholarly journals Numerical Computation and Stability Analysis for the Fractional Subdiffusions with Spatial Variable Coefficients

2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Lei Ren
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Fourth Order ◽  
Difference Method ◽  
Variable Coefficients ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Approximation Formula ◽  
Compact Finite Difference ◽  
Compact Finite Difference Method

In this paper, we propose an efficient compact finite difference method for a class of time-fractional subdiffusion equations with spatially variable coefficients. Based on the L2-1σ approximation formula of the time-fractional derivative and a fourth-order compact finite difference approximation to the spatial derivative, an efficient compact finite difference method is developed. The local truncation error and the solvability of the developed method are discussed in detail. The unconditional stability of the resulting scheme and also its convergence of second-order in time and fourth-order in space are rigorously proved using a discrete energy analysis method. Numerical examples are provided to demonstrate the accuracy and the theoretical results.

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