NUMERICAL APPROXIMATION OF THE PHASE-FIELD TRANSITION SYSTEM WITH NON-HOMOGENEOUS CAUCHY-NEUMANN BOUNDARY CONDITIONS IN BOTH UNKNOWN FUNCTIONS VIA FRACTIONAL STEPS METHOD

Armel Andami Ovono

doi:10.11948/2013028

2013 Volume 3 Issue 4

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Armel Andami Ovono. NUMERICAL APPROXIMATION OF THE PHASE-FIELD TRANSITION SYSTEM WITH NON-HOMOGENEOUS CAUCHY-NEUMANN BOUNDARY CONDITIONS IN BOTH UNKNOWN FUNCTIONS VIA FRACTIONAL STEPS METHOD[J]. Journal of Applied Analysis & Computation, 2013, 3(4): 377-397. doi: 10.11948/2013028

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Armel Andami Ovono. NUMERICAL APPROXIMATION OF THE PHASE-FIELD TRANSITION SYSTEM WITH NON-HOMOGENEOUS CAUCHY-NEUMANN BOUNDARY CONDITIONS IN BOTH UNKNOWN FUNCTIONS VIA FRACTIONAL STEPS METHOD[J]. Journal of Applied Analysis & Computation, 2013, 3(4): 377-397. doi: 10.11948/2013028

NUMERICAL APPROXIMATION OF THE PHASE-FIELD TRANSITION SYSTEM WITH NON-HOMOGENEOUS CAUCHY-NEUMANN BOUNDARY CONDITIONS IN BOTH UNKNOWN FUNCTIONS VIA FRACTIONAL STEPS METHOD

Armel Andami Ovono

Université des Sciences et Techniques de Masuku BP:943 Franceville, Gabon

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Abstract

Abstract

The paper concerns with the proof of the convergence for an iterative scheme of fractional steps type associated to the phase-field transition system endowed with non-homogeneous Cauchy-Neumann boundary conditions, in both unknown functions. The advantage of such method consists in simplifying the numerical computation necessary to be done in order to approximate the solution of nonlinear parabolic system. On the basis of this approach, a numerical algorithm in 2D case is introduced and an industrial implementation is made.
MSC: 35K55;65N12;65N30;80AXX

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