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Numerical Methods for PDEs: In Occasion of Raytcho Lazarov's 70th Birthday

Hristo Kojouharov, University of Texas at Arlington
Dynamically Consistent Numerical Schemes for Microbial Population Models


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.