Numerical simulation for the variable-order Galilei invariant advection diffusion equation with a nonlinear source term |
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Authors: | Chang-Ming ChenF. Liu V. AnhI. Turner |
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Affiliation: | a School of Mathematical Sciences, Xiamen University, Xiamen 361005, China b School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld. 4001, Australia |
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Abstract: | In this paper, we consider the variable-order Galilei advection diffusion equation with a nonlinear source term. A numerical scheme with first order temporal accuracy and second order spatial accuracy is developed to simulate the equation. The stability and convergence of the numerical scheme are analyzed. Besides, another numerical scheme for improving temporal accuracy is also developed. Finally, some numerical examples are given and the results demonstrate the effectiveness of theoretical analysis. |
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Keywords: | The variable-order Galilei invariant advection diffusion equation with a nonlinear source term The variable-order Riemann-Liouville fractional partial derivative Stability Convergence Numerical scheme improving temporal accuracy |
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