(untitled) (Journal of Computational Mathematics, 2023)
In this paper, ETD3-Pad00e9 and ETD4-Pad00e9 Galerkin finite element methods are proposed and analyzed for nonlinear delayed convection-diffusion-reaction equations with Dirichlet boundary conditions. An ETD-based RK is used for time integration of the corresponding equation. To overcome a well-known difficulty of numerical instability associated with the computation of the exponential operator, the Pad00e9 approach is used for such an exponential operator approximation, which in turn leads to the corresponding ETD-Pad00e9 schemes. An unconditional L^2 numerical stability is proved for the proposed numerical schemes, under a global Lipshitz continuity assumption. In addition, optimal rate error estimates are provided, which gives the convergence order of O(k^3+h^r) (ETD3-Pad00e9) or O(k^4+h^r) (ETD4-Pad00e9) in the L^2 norm, respectively. Numerical experiments are presented to demonstrate the robustness of the proposed numerical schemes.