A second-order compact difference scheme for the fourth-order fractional sub-diffusion equation

2017 ◽  
Vol 76 (2) ◽  
pp. 573-598 ◽  
Author(s):  
Pu Zhang ◽  
Hai Pu
Keyword(s):  
Diffusion Equation ◽  
Difference Scheme ◽  
Fourth Order ◽  
Second Order ◽  
Compact Difference Scheme ◽  
Compact Difference

scholarly journals A fast compact difference scheme for the fourth-order multi-term fractional sub-diffusion equation with non-smooth solution

Filomat ◽  
2021 ◽  
Vol 35 (5) ◽  
pp. 1495-1509
Author(s):  
Dakang Cen ◽  
Zhibo Wang ◽  
Yan Mo
Keyword(s):  
Diffusion Equation ◽  
Boundary Conditions ◽  
Difference Scheme ◽  
Fourth Order ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Stability And Convergence ◽  
Compact Difference Scheme ◽  
Compact Difference ◽  
Graded Meshes

In this paper, we develop a fast compact difference scheme for the fourth-order multi-term fractional sub-diffusion equation with Neumann boundary conditions. Combining L1 formula on graded meshes and the efficient sum-of-exponentials approximation to the kernels, the proposed scheme recovers the losing temporal convergence accuracy and spares the computational costs. Meanwhile, difficulty caused by the Neumann boundary conditions and fourth-order derivative is also carefully handled. The unique solvability, unconditional stability and convergence of the proposed scheme are analyzed by the energy method. At last, the theoretical results are verified by numerical experiments.

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