A compact Crank–Nicholson scheme for the numerical solution of fuzzy time fractional diffusion equations

2019 ◽  
Vol 32 (10) ◽  
pp. 6405-6412
Author(s):  
Hamzeh Zureigat ◽  
Ahmad Izani Ismail ◽  
Saratha Sathasivam
Keyword(s):  
Numerical Solution ◽  
Fractional Diffusion ◽  
Diffusion Equations ◽  
Fractional Diffusion Equations

scholarly journals Stochastic model for multi-term time-fractional diffusion equations with noise

2021 ◽  
Vol 25 (Spec. issue 2) ◽  
pp. 287-293
Author(s):  
Vahid Hosseini ◽  
Mohamad Remazani ◽  
Wennan Zou ◽  
Seddigheh Banihashemii
Keyword(s):  
Numerical Solution ◽  
Numerical Approach ◽  
Fractional Diffusion ◽  
Diffusion Equations ◽  
Data Driven ◽  
Algebraic Equations ◽  
Fractional Diffusion Equations ◽  
Collocation Points ◽  
Linear Algebraic Equations ◽  
Collocation Approach

This paper studies a spectral collocation approach for evaluating the numerical solution of the stochastic multi-term time-fractional diffusion equations associated with noisy data driven by Brownian motion. This model describes the symmetry breaking in molecular vibrations. The numerical solution of the stochastic multi-term time-fractional diffusion equations is proposed by means of collocation points method based on sixth-kind Chebyshev polynomial approach. For this purpose, the problem under consideration is reduced to a system of linear algebraic equations. Two examples highlight the robustness and accuracy of the proposed numerical approach.

scholarly journals A numerical solution for a class of time fractional diffusion equations with delay

2017 ◽  
Vol 27 (3) ◽  
pp. 477-488 ◽  
Author(s):  
Vladimir G. Pimenov ◽  
Ahmed S. Hendy
Keyword(s):  
Numerical Solution ◽  
Numerical Experiments ◽  
Numerical Scheme ◽  
Fixed Time ◽  
Fractional Diffusion ◽  
Diffusion Equations ◽  
Discrete Energy ◽  
Fractional Diffusion Equations ◽  
Equations With Delay ◽  
Theoretical Results

AbstractThis paper describes a numerical scheme for a class of fractional diffusion equations with fixed time delay. The study focuses on the uniqueness, convergence and stability of the resulting numerical solution by means of the discrete energy method. The derivation of a linearized difference scheme with convergence orderO(τ2−α+h4) in L∞-norm is the main purpose of this study. Numerical experiments are carried out to support the obtained theoretical results.

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