Abstract In this paper, a second order accurate time and space difference method is proposed to solve the nonlinear two-sided space-fractional diffusion equation with variable coefficients. We combine the alternating direction implicit method and Bi-conjugate gradient stabilized iterative solver to develop an efficient numerical method for a two dimensional, nonlinear, two-sided space-fractional diffusion equation with variable coefficients. Furthermore, the proposed method is proved to be uniquely solvable, stable and convergent. Finally, some numerical results verify the accuracy and efficiency of our computational approach.

中文翻译：

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变系数非线性双边空间分数扩散方程的有效数值方法

摘要 本文提出了一种求解变系数非线性双边空间分数扩散方程的二阶精确时空差分法。我们将交替方向隐式方法和双共轭梯度稳定迭代求解器相结合，为具有可变系数的二维、非线性、双边空间分数扩散方程开发了一种有效的数值方法。此外，所提出的方法被证明是唯一可解的、稳定的和收敛的。最后，一些数值结果验证了我们计算方法的准确性和效率。