The Chebyshev collocation method for a class of time fractional convection‐diffusion equation with variable coefficients

2021 ◽  
Author(s):  
Vijay Saw ◽  
Sushil Kumar
Keyword(s):  
Diffusion Equation ◽  
Collocation Method ◽  
Variable Coefficients ◽  
Chebyshev Collocation Method ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Chebyshev Collocation

Wavelet method for a class of fractional convection-diffusion equation with variable coefficients

2010 ◽  
Vol 1 (3) ◽  
pp. 146-149 ◽  
Author(s):  
Yiming Chen ◽  
Yongbing Wu ◽  
Yuhuan Cui ◽  
Zhuangzhuang Wang ◽  
Dongmei Jin
Keyword(s):  
Diffusion Equation ◽  
Variable Coefficients ◽  
Wavelet Method ◽  
Convection Diffusion ◽  
Convection Diffusion Equation

scholarly journals DOUBLE EXPONENTIAL EULER–SINC COLLOCATION METHOD FOR A TIME–FRACTIONAL CONVECTION–DIFFUSION EQUATION

2019 ◽  
pp. 745
Author(s):  
Ali Eftekhari
Keyword(s):  
Diffusion Equation ◽  
Collocation Method ◽  
Euler Polynomials ◽  
Algebraic Equations ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Linear Algebraic Equations ◽  
Double Exponential ◽  
Sinc Functions ◽  
Time Fractional Derivative

In this research, a new version of Sinc-collocation method incorporated with a Double Exponential (DE) transformation is implemented for a class of convectiondiffusion equations that involve time fractional derivative in the Caputo sense. Our approach uses the DE Sinc functions in space and the Euler polynomials in time, respectively. The problem is reduced to the solution of a system of linear algebraic equations. A comparison between the proposed approximated solution and numerical/exact/available solution reveals the reliability and significant advantages of our newly proposed method.

scholarly journals Sinc-Galerkin method for solving the time fractional convection–diffusion equation with variable coefficients

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Li Juan Chen ◽  
MingZhu Li ◽  
Qiang Xu
Keyword(s):  
Diffusion Equation ◽  
Galerkin Method ◽  
Numerical Scheme ◽  
Variable Coefficients ◽  
Exponential Rate ◽  
Order Accuracy ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Exponential Rate Of Convergence ◽  
Time Fractional Derivative

Abstract In this paper, a new numerical algorithm for solving the time fractional convection–diffusion equation with variable coefficients is proposed. The time fractional derivative is estimated using the $L_{1}$ L 1 formula, and the spatial derivative is discretized by the sinc-Galerkin method. The convergence analysis of this method is investigated in detail. The numerical solution is $2-\alpha$ 2 − α order accuracy in time and exponential rate of convergence in space. Finally, some numerical examples are given to show the effectiveness of the numerical scheme.

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