We couple the L1 discretization for Caputo derivative in time with spectral Galerkin method in space to devise a scheme that solves strongly nonlinear subdiffusion equations. Both the diffusivity and the source are allowed to be nonlinear functions of the solution. We prove method's stability and convergence with order $2-\alpha$ in time and spectral accuracy in space. Further, we illustrate our results with numerical simulations that utilize parallelism for spatial discretization. Moreover, as a side result we find asymptotic exact values of error constants along with their remainders for discretizations of Caputo derivative and fractional integrals. These constants are the smallest possible which improves the previously established results from the literature.

翻译：我们同时将卡普托衍生物的L1离散和空间的光谱加列金方法结合起来,以设计一个方案来解决强烈的非线性子扩散方程式。 允许 diffusiversity 和 源为解决方案的非线性函数 。 我们证明方法在时间和空间光谱精度方面与 $2\ alpha$ 的顺序具有稳定性和趋同性 。 此外, 我们用数字模拟来说明我们的结果, 这些模拟利用平行空间离散法。 此外, 作为副结果, 我们发现误差常数及其剩余值与卡普托衍生物和分集体分解的剩余值无症状的精确值。 这些常数是改进文献先前确定的结果的最小的常数 。