A new analytical technique of the L-type difference schemes for time fractional mixed sub-diffusion and diffusion-wave equations

2020 ◽  
Vol 102 ◽  
pp. 106115 ◽  
Author(s):  
Zhi-zhong Sun ◽  
Cui-cui Ji ◽  
Ruilian Du
Keyword(s):  
Wave Equations ◽  
Difference Schemes ◽  
Diffusion Wave ◽  
Analytical Technique ◽  
And Diffusion

On an Explicit Difference Method for Fractional Diffusion and Diffusion-Wave Equations

2009 ◽  
Author(s):  
Joaqui´n Quintana Murillo ◽  
Santos Bravo Yuste
Keyword(s):  
Wave Equations ◽  
Its Region ◽  
Fractional Diffusion ◽  
Diffusion Wave ◽  
Von Neumann ◽  
Stability Bound ◽  
Riemann Zeta ◽  
The Stability ◽  
And Diffusion ◽  
Explicit Difference Schemes

An explicit difference scheme for solving fractional diffusion and fractional diffusion-wave equations, in which the fractional derivative is in the Caputo form, is considered. The two equations are studied separately: for the fractional diffusion equation, the L1 discretization formula is employed, whereas the L2 discretization formula is used for the fractional diffusion-wave equation. Its accuracy is similar to other well-known explicit difference schemes, but its region of stability is larger. The stability analysis is carried out by means of a procedure similar to the standard von Neumann method. The stability bound, which is given in terms of the the Riemann Zeta function, is checked numerically.

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