A monotone approximation for a size-structured population model with a generalized environment

References

• Ackleh , A. S. and Deng , K. 2000 . Existence-uniqueness of solutions for a nonlinear nonautonomous size-structured population model: an upper-lower solution approach . Canadian Applied Mathematics Quarterly , 8 : 1 – 15 .
   Google Scholar
• Calsina , A. and El odrissi , O. 2002 . Asymptotic behavior of a semilinear age-structured population model with a dynamics for the resource . Mathematical, Computer Modeling , 35 : 403 – 427 .
   Google Scholar
• Calsina , A. and Saldana , J. 1997 . Asymptotic behavior of a model of hierarchically structured population dynamics . Journal of Mathematical Biology , 35 : 967 – 987 .
   Web of Science ®Google Scholar
• Clemons , C. B. , Hariharan , S. I. and Quinn , D. D. 2001 . Amplitude equations for time-dependent solutions of the McKendrick equations . SIAM Journal of Applied Mathematics , 62 : 684 – 705 .
   Web of Science ®Google Scholar
• Gurtin , M. and MacCamy , R. C. 1974 . Nonlinear age-dependent population dynamics . Archive for Rational Mechanics and Analysis , 54 : 281 – 300 .
   Web of Science ®Google Scholar
• Kraev , E. A. 2001 . Existence and uniqueness for height structured hierarchical population models . Natural Resource Modeling , 14 : 45 – 70 .
   Google Scholar
• Tucker , S. I. and Zimmerman , S. O. 1988 . A nonlinear model of population dynamics containing an arbitrary number of continuous structure variables . SIAM Journal of Applied Mathematics , 48 : 549 – 591 .
   Web of Science ®Google Scholar
• Lomnicki , A. 1998 . Population Ecology of Individuals, Monographs in Population Biology, 25 , Princeton : Princeton University Press .
   Google Scholar
• Ackleh , A. S. and Deng , K. 2005 . Monotone approximation for a hierarchical age-structured population model . Continuous and Discrete Impulse Systems Series B , 12 : 203 – 214 .
   Google Scholar
• Cushing , J. 1994 . The dynamics of hierarchical age-structured populations . Journal of Mathematical Biology , 32 : 705 – 729 .
   Web of Science ®Google Scholar
• Ackleh , A. S. , Deng , K. and Hu , S. 2005 . A quasilinear hierarchical size-structured model: well-posedness and approximation . Applied Mathematics and Optimization , 51 : 35 – 59 .
   Web of Science ®Google Scholar
• Ackleh , A. S. and Deng , K. 1997 . Monotone method for first order nonlocal hyperbolic initial-boundary value problems . Applicable Analysis , 67 : 283 – 293 .
   Google Scholar
• Ackleh , A. S. and Deng , K. 2000 . A monotone approximation for a nonlinear nonautonomous size-structured population model . Applied Mathematics and Computation , 108 : 103 – 113 .
   Web of Science ®Google Scholar
• Bellman , R. 1973 . Methods of Nonlinear Analysis , Vol. II , New York : Academic Press .
   Google Scholar
• Ladde , G. S. , Lakshmikantham , V. and Vatsala , A. S. 1985 . Monotone Iterative Techniques for Nonlinear Differential Equations , Boston : Pitman .
   Google Scholar
• Pao , C. V. 1992 . Nonlinear Parabolic and Elliptic Equations , New York : Plenum Press .
   Google Scholar
• Ackleh , A. S. and Deng , K. 1999 . A monotone approxiamtion for the non-autonomous size-structured population model . Quarterly Applied Mathematics , 57 : 261 – 267 .
   Web of Science ®Google Scholar
• Abia , L. M. , Angulo , O. and López-Marcos , J. C. 2004 . Size-structured population dynamics models and their numerical solutions . Discrete and Continuous Dynamical Systems Series Ba , 4 : 1203 – 1222 .
   Web of Science ®Google Scholar
• Ackleh , A. S. and Ito , K. 1997 . An implicit finite difference scheme for the nonlinear size-structured population Model . Numerical Functional Analysis and Optimization , 18 : 865 – 884 .
   Web of Science ®Google Scholar
• Angulo , O. and López-Marcos , J. C. 2004 . Numerical integration of fully nonlinear size structured population models . Applied Numerical Mathematics , 50 : 291 – 327 .
   Web of Science ®Google Scholar
• Angulo , O. and López-Marcos , J. C. Numerical integration of a size-structured cell population model in an environment of changing substrate concentration . Proceedings of the International Conference on Computational Methods in Sciences and Engineering . Kastoria, Greece. Vol. 1 , pp. 28 – 32 .
   Google Scholar
• Fairweather , G. and López-Marcos , J. C. 1994 . An explicit extrapolated box scheme for the Gurtin–MacCamy equation . Computers & Mathematics with Applications , 27 : 41 – 53 .
   Web of Science ®Google Scholar
• Ito , K. , Kappel , F. and Peichl , G. 1991 . A fully discretized approximation scheme for size-structured population models . SIAM Journal of Numerical Analysis , 28 : 923 – 954 .
   Web of Science ®Google Scholar
• Kostova , T. 2003 . An explicit third-order numerical method for size-structured population equations . Numerical Methods for Partial Differential Equations , 19 : 1 – 21 .
   Web of Science ®Google Scholar
• Sulsky , D. 1993 . Numerical solution of structured population models, I, Age structure . Journal of Mathematical Biology , 31 : 817 – 839 .
   PubMed Web of Science ®Google Scholar
• Sulsky , D. 1994 . Numerical solution of structured population models, II, Mass structure . Journal of Mathematical Biology , 32 : 491 – 514 .
   Web of Science ®Google Scholar