This paper is concerned with the numerical treatment of delay reaction-diffusion with the Dirichlet boundary condition. The finite element method with linear B-spline basis functions is utilized to discretize the space variable. The Crank-Nicolson method is used for the processes of time discretization. Sufficient and necessary conditions for the numerical method to be asymptotically stable are investigated. The convergence of the numerical method is studied. Some numerical experiments are performed to verify the applicability of the numerical method.
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Lubo, G. T., & Duressa, G. F. (2023). Linear B-spline finite element Method for solving delay reaction diffusion equation. Computational Methods for Differential Equations, 11(1), 161-174. doi: 10.22034/cmde.2022.49678.2066
MLA
Gemeda Tolessa Lubo; Gemechis File Duressa. "Linear B-spline finite element Method for solving delay reaction diffusion equation". Computational Methods for Differential Equations, 11, 1, 2023, 161-174. doi: 10.22034/cmde.2022.49678.2066
HARVARD
Lubo, G. T., Duressa, G. F. (2023). 'Linear B-spline finite element Method for solving delay reaction diffusion equation', Computational Methods for Differential Equations, 11(1), pp. 161-174. doi: 10.22034/cmde.2022.49678.2066
VANCOUVER
Lubo, G. T., Duressa, G. F. Linear B-spline finite element Method for solving delay reaction diffusion equation. Computational Methods for Differential Equations, 2023; 11(1): 161-174. doi: 10.22034/cmde.2022.49678.2066