Fractional Steps Scheme to Approximate the Phase-Field Transition System with Non-Homogeneous Cauchy–Neumann Boundary Conditions

Abstract

The paper presents a proof of the convergence for an iterative scheme of fractional steps type associated to the phase-field transition system (a nonlinear parabolic system) with non-homogeneous Cauchy–Neumann boundary conditions. The advantage of such method consists in simplifying the numerical computation necessary to be done in order to approximate the solution of a nonlinear parabolic system. On the basis of this approach, a numerical algorithm in the two dimensional case is introduced and an industrial implementation is made.