The propagation of the spiral waves in excitable media is governed by the non-linear reaction-diffusion equations. In order to solve these equations in the three-dimensional space, two methods have been implemented and parallelized on both shared-and distributed-memory computers. These implicit methods linearize the equations in time, following alternate directions in the first case (ADI), and using the Crank-Nicolson discretization in the second case. A linear system of algebraic equations has

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... been obtained and it has been solved using direct methods in the ADI technique, while in the second case has been used the conjugated gradient (CG) method. An optimized version of the CG algorithm is presented here, in which the largest efficiency has been obtained.