title: Asymptotic Expansion Method with Respect to Small Parameter for Ternary Diffusion Models.
abstract: Ternary diffusion models lead to strongly coupled systems of PDEs. We choose the smallest diffusion coefficient as a small parameter in a power series expansion whose components fulfill relatively simple equations. Although this series is divergent, one can use its finite sums to derive feasible numerical approximations, e.g. finite difference methods (FDMs).
authors.affiliation: Faculty of Materials Science and Ceramics, AGH University of Science and Technology, 30 Mickiewicza Av., 30-059, Krakow, Poland.
authors.forename: Marek
authors.initials: M
authors.lastname: Danielewski
authors.affiliation: Institute of Mathematics, University of Gdańsk, Wit Stwosz Street 57, 80-952, Gdańsk, Poland.
authors.forename: Henryk
authors.initials: H
authors.lastname: Leszczyński
authors.affiliation: Department of Differential Equations and Mathematics Applications, Gdańsk University of Technology, G. Narutowicz Street 11/12, 80-233, Gdańsk, Poland. aszafranska@mif.pg.gda.pl.
authors.forename: Anna
authors.initials: A
authors.lastname: Szafrańska
mesh_terms: D003198:Computer Simulation; D004058:Diffusion; D008962:Models, Theoretical
keywords: Asymptotic series expansion; Difference scheme; Diffusion; Mass conservation; Small parameter