Geodesic
Mathematical study of two-variable systems with adaptive numerical methods
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 19 (2016) no. 3, pp. 281-295

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In this paper, we consider reaction-diffusion systems arising from two-component predator-prey models with Smith growth functional response. The mathematical approach used here is twofold, since the time-dependent partial differential equations consist of both linear and nonlinear terms. We discretize the stiff or moderately stiff term with a fourth-order difference operator, advance the resulting nonlinear system of ordinary differential equations with a family of two competing exponential time differencing (ETD) schemes, and analyze them for stability. A numerical comparison of these two methods for solving various predator-prey population models with functional responses is also presented. Numerical results show that the techniques require less computational work. Also in the numerical results, some emerging spatial patterns are unveiled. 
@article{SJVM_2016_19_3_a3,
     author = {Kolade M. Owolabi},
     title = {Mathematical study of two-variable systems with adaptive numerical methods},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {281--295},
     publisher = {mathdoc},
     volume = {19},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2016_19_3_a3/}
}
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Kolade M. Owolabi. Mathematical study of two-variable systems with adaptive numerical methods. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 19 (2016) no. 3, pp. 281-295. http://geodesic.mathdoc.fr/item/SJVM_2016_19_3_a3/