Uniformly Convergent Time-fractional Reaction-Diffusion Equation
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Authors: F. E. MERGA AND G. F. DURESSA
DOI: 10.46793/KgJMat2607.1183M
Abstract:
In this paper, singularly perturbed time-fractional parabolic reaction-diffusion of initial boundary value problem is studied. The time-fractional derivative is applied in the Caputo fractional sense and handled by implicit Euler method. The spatial derivative is approximated by fitted cubic B-spline collocation method on a uniform mesh. Convergence analysis of the scheme is conducted and it is accurate of order O(h2 + (Δt2−α)). To test the effectiveness of proposed method two model examples are considered. The results from the experiment confirm that the scheme is uniformly convergent and has twin layers at the end spatial domain.
Keywords:
Time-fractional, parabolic reaction-diffusion, fitted B-spline collocation method, convergence analysis.
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