Premium
Numerical analysis of heat and moisture transport with a finite difference method
Author(s) -
Li Buyang,
Sun Weiwei
Publication year - 2013
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21707
Subject(s) - mathematics , uniqueness , partial differential equation , finite difference coefficient , finite difference method , finite difference , nonlinear system , euler equations , mathematical analysis , backward euler method , parabolic partial differential equation , finite difference scheme , euler's formula , constant (computer programming) , finite element method , thermodynamics , mixed finite element method , physics , quantum mechanics , computer science , programming language
In this article, we study a system of nonlinear parabolic partial differential equations arising from the heat and moisture transport through textile materials with phase change. A splitting finite difference method with semi‐implicit Euler scheme in time direction is proposed for solving the system of equations. We prove the existence and uniqueness of a classical positive solution to the parabolic system as well as the existence and uniqueness of a positive solution to the splitting finite difference system. We provide optimal error estimates for the splitting finite difference system under the condition that the mesh size and time step size are smaller than a positive constant which solely depends upon the physical parameters involved. Numerical results are presented to confirm our theoretical analysis. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2013