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Articles 1 - 4 of 4
Full-Text Articles in Physical Sciences and Mathematics
A Generalized Method Of Undetermined Coefficients, James S. Cook, William J. Cook
A Generalized Method Of Undetermined Coefficients, James S. Cook, William J. Cook
CODEE Journal
The method of undetermined coefficients is used to solve constant coefficient nonhomogeneous differential equations whose forcing function is itself the solution of a homogeneous constant coefficient differential equation. In this paper, we show that the classical methods for tackling constant coefficient equations, including the method of undetermined coefficients, generalize to much wider class linear differential equations which, for example, include Cauchy-Euler type equations. This general method includes an explicit construction of the fundamental solution sets of such equations. We also briefly consider where this method can be applied by producing the most general second and third order differential equations that …
Maintaining Ecosystem And Economic Structure In A Three-Species Dynamical System In Chesapeake Bay, Maila Hallare, Iordanka Panayotova
Maintaining Ecosystem And Economic Structure In A Three-Species Dynamical System In Chesapeake Bay, Maila Hallare, Iordanka Panayotova
CODEE Journal
We consider a three-species fish dynamical system in Chesapeake Bay consisting of the Atlantic menhaden as the prey and its two competing predators, the striped bass and the catfish. Building on our previous work in this system, we consider the issue of balancing economic harvesting goals (financial gain for fishermen) with ecological harvesting goals (non-extinction of species). In particular, we investigate the bionomic equilibria, maximum sustainable yield, and the maximum economic yield. Analytical computations and numerical simulations are employed to provide some mathematical guidance on fisheries management policies.
Human Impact On Planetary Temperature And Glacial Volume: Extending A Toy Climate Model To A New Millennium, Samantha Secor, Jennifer Switkes
Human Impact On Planetary Temperature And Glacial Volume: Extending A Toy Climate Model To A New Millennium, Samantha Secor, Jennifer Switkes
CODEE Journal
Starting with a toy climate model from the literature, we employ a system of two nonlinear differential equations to model the reciprocal effects of the average temperature and the percentage of glacial volume on Earth. In the literature, this model is used to demonstrate the potential for a stable periodic orbit over a long time span in the form of an attracting limit cycle. In the roughly twenty five years since this model appeared in the literature, the effects of global warming and human-impacted climate change have become much more well known and apparent. We demonstrate modification of initial conditions …
Analysis Of A Mathematical Model Of Real-Time Competitive Binding On A Microarray, Frank H. Lynch
Analysis Of A Mathematical Model Of Real-Time Competitive Binding On A Microarray, Frank H. Lynch
CODEE Journal
A mathematical model of competitive binding on a microarray in real-time yields a planar system of nonlinear ordinary differential equations. This model can be used to explore dimensionless formulation, linear approximation, and reduction. Real-time competitive binding is proposed as an uncommon approach to advance the study of planar systems of differential equations.