Pointwise-in-time a posteriori error control for higher-order discretizations of time-fractional parabolic equations

Time-fractional parabolic equations with a Caputo time derivative are considered. For such equations, we explore and further develop the new methodology of a-posteriori error estimation adaptive stepping proposed in Kopteva (2022). We improve earlier algorithm based on this theory, specifically address its stable efficient implementation context high-order methods. The considered methods include an L1-2 method continuous collocation arbitrary order, for which temporal meshes shown to yield optimal convergence rates presence solution singularities.