In this paper, we present a compact finite difference method for a class
of fourth-order nonlinear neutral delay sub-diffusion equations in two-dimensional space. The fourth-order problem is first
transformed into a second-order system by a reduced-order method. Next by
using compact operator to approximate the second order space derivatives and
L2-1σ formula to approximate the time
fractional derivative, the difference scheme which is fourth order in space and
second order in time is obtained. Then, the existence and uniqueness of
solution, the convergence rate of and the stability of
the scheme are proved. Finally, numerical results are given to verify the
accuracy and validity of the scheme.
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