caa a22 4500 467939284 CHVBK 20180406153007.0 cr unu---uuuuu 170328e20061101xx s 000 0 eng 10.1007/s10444-004-7639-7 doi (NATIONALLICENCE)springer-10.1007/s10444-004-7639-7 Kim M. Department of Mathematics, Inha University, 402-751, Inchon, South Korea aut Global dynamics of approximate solutions to an age-structured epidemic model with diffusion [Elektronische Daten] [M. Kim] We consider an age-dependent s-i-s epidemic model with diffusion whose mortality is unbounded. We approximate the solution using Galerkin methods in the space variable combined with backward Euler along the characteristic direction in the age and time variables. It is proven that the scheme is stable and convergent in optimal rate in l ∞,2 (L 2) norm. To investigate the global behavior of the discrete solution resulting from the algorithm, we reformulate the resulting system into a monotone form. Positivity of the nonlocal birth process is proved using the positivity of the first eigenvalue of the resulting matrix system and using the fact that the positivity is preserved along the characteristics. The difference equation of the steady state coupled with nonlocal birth process is solved by developing monotone iterative schemes. The stability of the discrete solution of the steady state is then analyzed by constructing suitable positive subsolutions. Springer, 2006 s - i - s epidemic model nationallicence integro-differential equation nationallicence Galerkin method nationallicence characteristic method nationallicence error estimates nationallicence asymptotic behavior nationallicence Advances in Computational Mathematics Springer Netherlands 25/4(2006-11-01), 451-474 1019-7168 25:4<451 2006 25 10444 https://doi.org/10.1007/s10444-004-7639-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10444-004-7639-7 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Kim M. Department of Mathematics, Inha University, 402-751, Inchon, South Korea aut NATIONALLICENCE 773 0- Advances in Computational Mathematics Springer Netherlands 25/4(2006-11-01), 451-474 1019-7168 25:4<451 2006 25 10444 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer