Fourth Kind Shifted Chebyshev Polynomials for Solving Space Fractional Order Advection–Dispersion Equation Based on Collocation Method and Finite Difference Approximation

2018 ◽  
Vol 4 (3) ◽  
Author(s):  
Vijay Saw ◽  
Sushil Kumar
Keyword(s):  
Finite Difference ◽  
Dispersion Equation ◽  
Collocation Method ◽  
Fractional Order ◽  
Chebyshev Polynomials ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Advection Dispersion ◽  
Fourth Kind

scholarly journals Stable and Efficient Modeling of Anelastic Attenuation in Seismic Wave Propagation

2012 ◽  
Vol 12 (1) ◽  
pp. 193-225 ◽  
Author(s):  
N. Anders Petersson ◽  
Björn Sjögreen
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Half Space ◽  
Material Model ◽  
Second Order ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Space Problem ◽  
Standard Linear Solid ◽  
Standard Linear

AbstractWe develop a stable finite difference approximation of the three-dimensional viscoelastic wave equation. The material model is a super-imposition of N standard linear solid mechanisms, which commonly is used in seismology to model a material with constant quality factor Q. The proposed scheme discretizes the governing equations in second order displacement formulation using 3N memory variables, making it significantly more memory efficient than the commonly used first order velocity-stress formulation. The new scheme is a generalization of our energy conserving finite difference scheme for the elastic wave equation in second order formulation [SIAM J. Numer. Anal., 45 (2007), pp. 1902-1936]. Our main result is a proof that the proposed discretization is energy stable, even in the case of variable material properties. The proof relies on the summation-by-parts property of the discretization. The new scheme is implemented with grid refinement with hanging nodes on the interface. Numerical experiments verify the accuracy and stability of the new scheme. Semi-analytical solutions for a half-space problem and the LOH.3 layer over half-space problem are used to demonstrate how the number of viscoelastic mechanisms and the grid resolution influence the accuracy. We find that three standard linear solid mechanisms usually are sufficient to make the modeling error smaller than the discretization error.

scholarly journals On the finite difference approximation for a parabolic blow-up problem

2007 ◽  
Vol 24 (2) ◽  
pp. 131-160 ◽  
Author(s):  
C. -H. Cho ◽  
S. Hamada ◽  
H. Okamoto
Keyword(s):  
Finite Difference ◽  
Blow Up ◽  
Finite Difference Approximation ◽  
Difference Approximation
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