caa a22 4500 605497184 CHVBK 20210128100540.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s10543-014-0509-x doi (NATIONALLICENCE)springer-10.1007/s10543-014-0509-x Stability analysis of Crank-Nicolson and Euler schemes for time-dependent diffusion equations [Elektronische Daten] [Cassio Oishi, Jin Yuan, Jose Cuminato, David Stewart] In this paper, we study the stability of the Crank-Nicolson and Euler schemes for time-dependent diffusion coefficient equations on a staggered grid with explicit and implicit approximations to the Dirichlet boundary conditions. Using the matrix representation for the numerical scheme and boundary conditions it is shown that for implicit boundary conditions the Crank-Nicolson scheme is unrestrictedly stable while it becomes conditionally stable for explicit boundary conditions. Numerical examples are provided illustrating this behavior. For the Euler schemes the results are similar to those for the constant coefficient case. The implicit Euler with implicit or explicit boundary conditions is unrestrictedly stable while the explicit Euler with explicit boundary conditions presents the usual stability restriction on the time step. Springer Science+Business Media Dordrecht, 2014 Stability analysis nationallicence Crank-Nicolson scheme nationallicence Staggered grids nationallicence Boundary conditions nationallicence Non-constant coefficient diffusion equations nationallicence Oishi Cassio Departamento de Matemática, e Computação, Universidade Estadual Paulista, Presidente Prudente, Brazil aut Yuan Jin Departamento de Matemática, Universidade Federal do Paraná, Curitiba, Brazil aut Cuminato Jose Departamento de Matemática Aplicada e Estatística, Universidade de São Paulo, São Carlos, Brazil aut Stewart David Department of Mathematics, University of Iowa, Iowa City, USA aut BIT Numerical Mathematics Springer Netherlands 55/2(2015-06-01), 487-513 0006-3835 55:2<487 2015 55 10543 https://doi.org/10.1007/s10543-014-0509-x text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10543-014-0509-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Oishi Cassio Departamento de Matemática, e Computação, Universidade Estadual Paulista, Presidente Prudente, Brazil aut NATIONALLICENCE 700 1- Yuan Jin Departamento de Matemática, Universidade Federal do Paraná, Curitiba, Brazil aut NATIONALLICENCE 700 1- Cuminato Jose Departamento de Matemática Aplicada e Estatística, Universidade de São Paulo, São Carlos, Brazil aut NATIONALLICENCE 700 1- Stewart David Department of Mathematics, University of Iowa, Iowa City, USA aut NATIONALLICENCE 773 0- BIT Numerical Mathematics Springer Netherlands 55/2(2015-06-01), 487-513 0006-3835 55:2<487 2015 55 10543