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Author:

Dai, Haishen (Dai, Haishen.) | Huang, Qiumei (Huang, Qiumei.) (Scholars:黄秋梅) | Wang, Cheng (Wang, Cheng.)

Indexed by:

Scopus SCIE

Abstract:

In this paper, ETD3-Pade and ETD4-Pade 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 Pade approach is used for such an exponential operator approximation, which in turn leads to the corresponding ETD-Pade 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-Pade) or O(k(4) + h(r)) (ETD4-Pade) in the L-2 norm, respectively. Numerical experiments are presented to demonstrate the robustness of the proposed numerical schemes.

Keyword:

Nonlinear delayed convection diffusion reaction equations Lipshitz continuity ETD-Pade scheme Convergence analysis and error estimate L-2 stability analysis

Author Community:

  • [ 1 ] [Dai, Haishen]Beijing Univ Technol, Fac Sci, Sch Math, Beijing 100124, Peoples R China
  • [ 2 ] [Huang, Qiumei]Beijing Univ Technol, Fac Sci, Sch Math, Beijing 100124, Peoples R China
  • [ 3 ] [Wang, Cheng]Univ Massachusetts, Dept Math, N Dartmouth, MA 02747 USA

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Source :

JOURNAL OF COMPUTATIONAL MATHEMATICS

ISSN: 0254-9409

Year: 2023

Issue: 3

Volume: 41

Page: 350-351

0 . 9 0 0

JCR@2022

ESI Discipline: MATHEMATICS;

ESI HC Threshold:9

Cited Count:

WoS CC Cited Count:

SCOPUS Cited Count: 2

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 1

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