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Question: Questions about dsolve(...,numeric), odeplot and DEplot (on the Lotka-Volterra eq.'s)

Question:Questions about dsolve(...,numeric), odeplot and DEplot (on the Lotka-Volterra eq.'s)

Mads Ravn 16 Maple
ode dsolve numeric deplot
November 28 2006
0
Hello all, I'm looking into visualizing/solving the Lotka-Volterra equations in Maple 10. In doing so I've run into a few problems: 1) When executing the following commands > odeqs:= {diff(N(t),t) = a*N(t) - b*N(t)*P(t), diff(P(t),t)=c*N(t)*P(t) - d*P(t)}: > # Growth rate of prey > a:= 3; > # Predatation rate > b:= 2; > # Growth of predators as a consequence of predation > c:= 1; > # Mortality rate of predators > d:= 1/2; > # Initial Conditions > initConds:=[N(0)=(5/3),P(0)=(10/9)]]; > > # Display number of prey as a function of time > DEplot(odeqs, [N(t),P(t)], t=0..100, N=0..7, P=0..7, initConds, stepsize=0.05,scene=[t,N(t)]): the last command will output an empty plot in Maple 10, while in older versions (9.5, at least) will display the desired graph. Turns out the culprit is scene=[t,N(t)]. Why is this not working? (I've looked at the "Updates to Differential Equation (DE) Solvers in Maple 10", "DEtools" and "DEplot" help pages, but no clues. I'm also aware of a workaround using dsolve(...,numeric) and odeplot) 2) Why will the following commands (with odeeqs and initConds given above) >Digits:=20: >numSol:=dsolve([op(odeeqs), op(initConds)],numeric): >p1:=odeplot(numSol,[[t,N(t),color=red]],t=0..100,legend=["Prey"],labels=["t","N"]); >p2:=odeplot(numSol,[[t,N(t),color=green]],t=0..200,legend=["Prey"],labels=["t","N"]); > display(p1,p2); provide wildly different solutions on the overlapping interval 0..100? I understand that the numeric solution is provide by RKF45 with a default absolute error less than 10^-7, but decreasing this changes nothing. Is this a numerical stability issue (Changing Digits to something else yields nothing)? Thanks, Mads
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