Numerical Algorithms with High Spatial Accuracy for the Fourth-Order Fractional Sub-Diffusion Equations with the First Dirichlet Boundary Conditions

摘要: In this paper, a compact algorithm for the fourth-order fractional sub-diffusion equations with first Dirichlet boundary conditions, which depict wave propagation in intense laser beams, is investigated. Combining average operator spatial derivative, L1 formula applied to approximate temporal Caputo derivative. A novel technique introduced deal conditions. Using mathematical induction method, we prove that presented difference scheme unconditionally stable and convergent by energy method. The convergence order $$O(\tau ^{2-\alpha }+h^4)$$O(?2-?+h4) $$L_2$$L2-norm. outline two-dimensional problem also considered. Finally, some numerical examples are provided confirm theoretical results.