scholarly journals A Compact Difference Scheme for Time-Fractional Dirichlet Biharmonic Equation on Temporal Graded Meshes

2021 ◽  
Vol 11 (1) ◽  
pp. 164-180
Author(s):  
Mingrong Cui
Keyword(s):  
Difference Scheme ◽  
Biharmonic Equation ◽  
Compact Difference Scheme ◽  
Compact Difference ◽  
Graded Meshes

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.

scholarly journals A Compact Difference Scheme for the Biharmonic Equation in Planar Irregular Domains

2009 ◽  
Vol 47 (4) ◽  
pp. 3087-3108 ◽  
Author(s):  
M. Ben-Artzi ◽  
I. Chorev ◽  
J.-P. Croisille ◽  
D. Fishelov
Keyword(s):  
Difference Scheme ◽  
Biharmonic Equation ◽  
Compact Difference Scheme ◽  
Irregular Domains ◽  
Compact Difference

Direct calculation of waves in fluid flows using high-order compact difference scheme

AIAA Journal ◽  
1994 ◽  
Vol 32 (9) ◽  
pp. 1766-1773 ◽  
Author(s):  
Sheng-Tao Yu ◽  
Lennart S. Hultgren ◽  
Nan-Suey Liu
Keyword(s):  
Difference Scheme ◽  
Fluid Flows ◽  
Direct Calculation ◽  
High Order ◽  
Compact Difference Scheme ◽  
Compact Difference
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