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Abstract:
In this paper, ETD3-Padé and ETD4-Padé 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 Padé approach is used for such an exponential operator approximation, which in turn leads to the corresponding ETD-Padé schemes. An unconditional L2 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(k3 + hr) (ETD3-Padé) or O(k4 + hr) (ETD4-Padé) in the L2 norm, respectively. Numerical experiments are presented to demonstrate the robustness of the proposed numerical schemes. © 2023 Global Science Press. All rights reserved.
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Source :
Journal of Computational Mathematics
ISSN: 0254-9409
Year: 2023
Issue: 3
Volume: 41
Page: 370-394
0 . 9 0 0
JCR@2022
ESI Discipline: MATHEMATICS;
ESI HC Threshold:9
Cited Count:
WoS CC Cited Count: 11
SCOPUS Cited Count: 2
ESI Highly Cited Papers on the List: 0 Unfold All
WanFang Cited Count:
Chinese Cited Count:
30 Days PV: 6
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