Sixth-order non-uniform combined compact difference scheme for multi-term time fractional diffusion-wave equation

2018 ◽  
Vol 131 ◽  
pp. 72-94 ◽  
Author(s):  
Z. Soori ◽  
A. Aminataei
Keyword(s):  
Wave Equation ◽  
Difference Scheme ◽  
Fractional Diffusion ◽  
Sixth Order ◽  
Compact Difference Scheme ◽  
Diffusion Wave ◽  
Compact Difference

scholarly journals Numerical Algorithms for the Fractional Diffusion-Wave Equation with Reaction Term

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Hengfei Ding ◽  
Changpin Li
Keyword(s):  
Wave Equation ◽  
Difference Scheme ◽  
Fourier Method ◽  
Numerical Algorithms ◽  
Fractional Diffusion ◽  
Second Order ◽  
Diffusion Wave ◽  
Order Difference ◽  
Reaction Term ◽  
Liouville Derivative

Two numerical algorithms are derived to compute the fractional diffusion-wave equation with a reaction term. Firstly, using the relations between Caputo and Riemann-Liouville derivatives, we get two equivalent forms of the original equation, where we approximate Riemann-Liouville derivative by a second-order difference scheme. Secondly, for second-order derivative in space dimension, we construct a fourth-order difference scheme in terms of the hyperbolic-trigonometric spline function. The stability analysis of the derived numerical methods is given by means of the fractional Fourier method. Finally, an illustrative example is presented to show that the numerical results are in good agreement with the theoretical analysis.

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