Numerical Methods for PDEs: In Occasion of Raytcho Lazarov's 70th Birthday
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- Texas A&M University
- College Station, TX
- Rudder Tower 701
- Hristo Kojouharov, University of Texas at Arlington
- Dynamically Consistent Numerical Schemes for Microbial Population Models
Abstract
Several different mathematical models of complex biological systems involving microbial populations are briefly discussed. In addition, a finite-difference approach is presented for solving the corresponding systems of differential equations. It is based on a nonlocal modeling of the nonlinear right-hand-side functions and a nonstandard discretization of the time-derivative. Positive and elementary-stable nonstandard (PESN) finite difference methods are also formulated and analyzed based on extensions of the nonstandard discretization rules. A series of numerical results are presented to demonstrate the performance of the proposed numerical methods.