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格式，并辅以快速无记忆实现方法。具体而言，我们给出了卷积求积可容许性的条件，并通过有限元方法对方程的空间部分进行离散化。我们证明了该格式的无条件稳定性和收敛性，并给出了误差界。作为中间结果，我们还获得了卷积求积的离散格朗沃尔不等式，这是基于能量法的收敛性证明中的关键要素。最后通过数值算例验证了收敛性，并展示了使用快速无记忆求积时计算时间的减少。