A FIRST-ORDER FRACTIONAL-STEPS-TYPE METHOD TO APPROXIMATE A NONLINEAR REACTION-DIFFUSION EQUATION WITH HOMOGENEOUS CAUCHY-NEUMANN BOUNDARY CONDITIONS

. In this present paper, we consider a nonlinear reaction-diffusion problem (1), endowed with a cubic nonlinear reaction term and homogeneous Cauchy-Neumann boundary conditions. We will approach the proposed nonlinear parabolic problem in the spirit of Hadamard's well-posedness conditions (see [26, p. 46]). Practically, we start our study by investigating the solvability of such a problem in the class W-p(1,2 )(Q), p >= 2. The second goal is to develop an iterative splitting scheme, corresponding to the nonlinear reaction-diffusion problem in question. Results about the convergence of the numerical scheme and error estimation are established, too. On the basis of the proposed numerical scheme, we formulate a conceptual algorithm GTanase- alg-frac rd CN-bc, which represents a delicate challenge for our future works, in order to approximate the solution of the nonlinear parabolic problem (1). The benefit of such a method aims at simplifying the process of numerical computations due to its decoupling feature.