We construct a Convolution Quadrature (CQ) scheme for the quasilinear subdiffusion equation and supply it with the fast and oblivious implementation. In particular we find a condition for the CQ to be admissible and discretize the spatial part of the equation with the Finite Element Method. We prove the unconditional stability and convergence of the scheme and find a bound on the error. As a passing result, we also obtain a discrete Gronwall inequality for the CQ, which is a crucial ingredient of our convergence proof based on the energy method. The paper is concluded with numerical examples verifying convergence and computation time reduction when using fast and oblivious quadrature.

翻译：我们针对拟线性次扩散方程构建了一种卷积求积（CQ）格式，并为其配备快速无记忆实现。特别地，我们给出了CQ格式可容许的条件，并采用有限元法对空间部分进行离散化。我们证明了该格式的无条件稳定性与收敛性，并给出了误差界。作为附带结果，我们还获得了CQ格式的离散Gronwall不等式，这是基于能量法的收敛性证明的关键要素。最后通过数值算例验证了收敛性及采用快速无记忆求积法带来的计算时间缩减效果。