Numerical Analysis of Local Discontinuous Galerkin Method for the Time-Fractional Fourth-Order Equation with Initial Singularity

In this paper, efficient methods seeking the numerical solution of a time-fractional fourth-order differential equation with Caputo’s derivative are derived. The such problem has weak singularity near initial time t=0. Caputo order α∈(0,1) is discretized by well-known L1 formula on nonuniform meshes; for spatial derivative, local discontinuous Galerkin (LDG) finite element method used. Based discrete fractional Gronwall’s inequality, we prove stability proposed scheme and optimal error estimate solution, i.e., (2−α)-order accurate in (k+1)-order space, when piece-wise polynomials degree at most k Moreover, second-order time-stepping developed model. uses L2-1σ LDG space approximation. temporal convergence also shown. Finally, some experiments presented to confirm theoretical results.