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This work is devoted to an optimized domain decomposition method applied to a non linear anisotropic reaction equation. The proposed method is based on the idea of the optimized of two order (OO2) method developed this last two decades. We first use a modified fixed point technique to linearize the problem in a way to converge fately, then we generalize the OO2 method and modify it to obtain a new more optimized rate of convergence of the Schwarz algorithm. To compute the new rate of convergence we have used Fourier analysis. For the numerical computation we minimize this rate of convergence using a global optimization algorithm. Several test-cases of analytical problems illustrate this approach and show the efficiency of the proposed new method.

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