  A fourth-order compact scheme is proposed for a fourth-order subdiffusion
equation with the first Dirichlet boundary conditions. The fourth-order problem
is firstly reduced into a couple of spatially second-order system and we use an
averaged operator to construct a fourth-order spatial approximation. This
averaged operator is compact since it involves only two grid points for the
derivative boundary conditions. The L1 formula on irregular mesh is considered
for the Caputo fractional derivative, so we can resolve the initial singularity
of solution by putting more grid points near the initial time. The stability
and convergence are established by using three theoretical tools: a
complementary discrete convolution kernel, a discrete fractional Gronwall
inequality and an error convolution structure. Some numerical experiments are
reported to demonstrate the accuracy and efficiency of our method.

Numerical Analysis;Numerical Analysis