Compact Difference Scheme for Time-Fractional Fourth-Order Equation with First Dirichlet Boundary Condition

Abstract

The convergence of a compact finite difference scheme for one- and two-dimensional time fractional fourth order equations with the first Dirichlet boundary conditions is studied. In one-dimensional case, a Hermite interpolating polynomial is used to transform the boundary conditions into the homogeneous ones. The Stephenson scheme is employed for the spatial derivatives discretisation. The approximate values of the normal derivative are obtained as a by-product of the method. For periodic problems, the stability of the method and its convergence with the accuracy $\mathcal{O}$(τ^2−$α$) + $\mathcal{O}$($h$⁴) are established, with the similar error estimates for two-dimensional problems. The results of numerical experiments are consistent with the theoretical findings.