Ionic models are used to describe the evolution of the electrical potential across the cardiac cell membranes. The Mitchell-Schaeffer model is a simple two variables nonlinear ionic model with a limited set of parameters. This model can still capture the main features of the cardiac action potential, namely the action potential duration (APD), the conduction velocity (CV), depolarisation time (DT), recovery time (RT), etc. In this paper we have developed an optimization method to recover the specific characteristics ADP, DT and RT by identifying the values that the four parameters τ = [τ in , τ out , τ open , τ close , σ] of the Mitchell-Schaeffer must take. By using the fonction ode in Scilab, Mitchell-Schaeffer model solutions have been oabtained numerically.

This paper refers to mathematical modelling and numerical analysis. The analysis to be presented through this paper deals with Robin’s problem which boundary equation is a linear combination of Dirichlet and Neumann-type boundary condi-tions. For this purpose we proved the existence and uniqueness of the solution. It is worth noting that the implementation of numerical simulations depends on the type of problem since it requires a search for explicit solution. Consequently, the motivation exists in this paper for choosing a classical method of variation of constants and employing a finite difference method to find the exact and numerical solutions, respectively so that numerical simulations were implemented in Scilab.

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This paper aims is to solve an advection problem where u=u(x, t) is the solution by Lax-Wendrof and finite difference methods, to study the analytical stability in L 2 [0, 1], L ∞ [0, 1], then calculate the truncation error of these methods and finally study the analytical convergence of these methods. These numerical techniques of resolution were implemented in Scilab.

In this paper we treat the existence, the uniqueness and the numerical resolution of the problem at the elliptic limits case of the Cauchy-Dirichlet problem of the type the stationary convection-diffusion equation. By applying the Lax-Milgram theorem, we proved the existence and the uniqueness of the problem, then we solved the problem numerically by the finite difference method. In addition, we solved the problem analytically using the method of variation of constants. Finally, we performed a numerical simulation of said problem to approach the exact solution by the numerical solution using the software Scilab