Second-Order Accurate Difference Methods for a One-Sex Model of Population Dynamics

1993 ◽  
Vol 30 (5) ◽  
pp. 1385-1399 ◽  
Author(s):  
Yonghoon Kwon ◽  
Chung-Ki Cho
Keyword(s):  
Population Dynamics ◽  
Second Order ◽  
Difference Methods

On the accuracy of some explicit and implicit methods for the inviscid GRLW equation subject to initial Gaussian conditions

2016 ◽  
Vol 26 (3/4) ◽  
pp. 698-721 ◽  
Author(s):  
J I Ramos
Keyword(s):  
Finite Difference ◽  
Fourth Order ◽  
Finite Difference Methods ◽  
Second Order ◽  
Time Step ◽  
Content Type ◽  
Difference Methods ◽  
Temporal And Spatial ◽  
Runge Kutta ◽  
Grlw Equation

Purpose – The purpose of this paper is to both determine the effects of the nonlinearity on the wave dynamics and assess the temporal and spatial accuracy of five finite difference methods for the solution of the inviscid generalized regularized long-wave (GRLW) equation subject to initial Gaussian conditions. Design/methodology/approach – Two implicit second- and fourth-order accurate finite difference methods and three Runge-Kutta procedures are introduced. The methods employ a new dependent variable which contains the wave amplitude and its second-order spatial derivative. Numerical experiments are reported for several temporal and spatial step sizes in order to assess their accuracy and the preservation of the first two invariants of the inviscid GRLW equation as functions of the spatial and temporal orders of accuracy, and thus determine the conditions under which grid-independent results are obtained. Findings – It has been found that the steepening of the wave increase as the nonlinearity exponent is increased and that the accuracy of the fourth-order Runge-Kutta method is comparable to that of a second-order implicit procedure for time steps smaller than 100th, and that only the fourth-order compact method is almost grid-independent if the time step is on the order of 1,000th and more than 5,000 grid points are used, because of the initial steepening of the initial profile, wave breakup and solitary wave propagation. Originality/value – This is the first study where an accuracy assessment of wave breakup of the inviscid GRLW equation subject to initial Gaussian conditions is reported.

scholarly journals Multiple-Stressor Interactions in Tributaries Alter Downstream Ecosystems in Stream Mesocosm Networks

Water ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1194
Author(s):  
Ana M. Chará-Serna ◽  
John S. Richardson
Keyword(s):  
Population Dynamics ◽  
Second Order ◽  
Physical Habitat ◽  
Stream Networks ◽  
Stream Network ◽  
Dispersal Patterns ◽  
Multiple Stressor ◽  
Ept Taxa ◽  
Stream Mesocosm ◽  
Ept Richness

We studied how multiple-stresssors in tributaries affect function, diversity, and physical habitat of recipient downstream ecosystems. Using a mesocosm model of a stream network, we manipulated sediment and nutrients individually and in combination in tributaries of second-order channels, to test the effect of complex stressor interactions within tributaries on recipient channels. Sedimentation in second-order channels increased with the level of disturbance of the tributaries. Moreover, Ephemeroptera, Plecoptera, and Trichoptera (EPT) density and EPT richness were higher in second-order channels fed by tributaries where the stressors were applied separately, compared to those fed by tributaries where the stressors were applied simultaneously. Our observations suggest this result was due to the combination of the two stressors within the same tributary reducing EPT drift from the tributaries further than the addition of the stressors in separate tributaries. These results support the hypothesis that cumulative upstream disturbance can influence downstream recipient ecosystems in stream networks. However, contrary to our expectations, most observed effects were due to impacts on dispersal patterns of EPT taxa, rather than downstream accumulation of disturbances throughout the network. Our results underscore the importance of metacommunity frameworks to understand how tributary disturbance may influence population dynamics in downstream ecosystems.

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