In this paper, we consider a variable-order fractional advection-diffusion equationudwith a nonlinear source term on a finite domain. Explicit and implicit Euler approximations for theudequation are proposed. Stability and convergence of the methods are discussed. Moreover, we alsoudpresent a fractional method of lines, a matrix transfer technique, and an extrapolation method forudthe equation. Some numerical examples are given, and the results demonstrate the effectiveness ofudtheoretical analysis.ud
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机译：在本文中，我们考虑在有限域上具有非线性源项的变分分数阶对流扩散方程 ud。提出了关于 dequequ的显式和隐式Euler近似。讨论了方法的稳定性和收敛性。此外，我们还给出了线的分数法，矩阵传递技术和方程的外推法。给出了一些数值例子，结果证明了理论分析的有效性。 ud
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