Abstract
We investigate in this paper, the approximation of a semi-linear system of reaction diffusion equations in a bounded domain. The system is discretized using a \({\mathbb{P}_r}\) Lagrange finite method in space, and an implicit finite difference scheme in time. We analyze the scheme stability in the space L ∞ ((0, T), L 2(Ω)) ∩ L 2((0, T), H 1(Ω)). The error norm for approximate solutions is of order O(h r + δ t).
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