7.114 bug in odeplot with Mac OS X, Maple 7 (8.9.02)

7.114.1 Roberto Sussman

I found a nasty plot using Maple 7 with a Mac (G4 Tower 400 Mhz, Mac OS X version 10.1). Since Maple is not native it runs under the "Classic" Mac OS 9.2 emulation.

First I run the following simple commands related to solving numericaly a system of two ODE’s

 > eqMN:=(beta0,lambda0,x)->diff(M(x),x)=piecewise(x>0, 
              x^2*(exp(beta0-beta(x))+lambda0), x=0, 0); 
 > eqbN:=(lambda0,x)->diff(beta(x),x)=piecewise(x>0, 
 > (M(x)/x^2-lambda0*x)*beta(x), x=0, 0); 
 > S0:=dsolve({eqMN(10^6,0,x),eqbN(0,x),M(0)=0,beta(0)=10^6}, 
              {M(x),beta(x)},type=numeric); 
 > seq(S0(.5*i), i=1..5); 
 > plots[odeplot](S0,[x,log10(M(x))],0..2.5,color=black);
 

Up to this point everything is fine. But then, I want to redo the ODE’s with a different method, therefore I edit the dsolve commands adding (say) "method = lsode" (the problem is independent of the method).

I do so and then re-run all the commands. It does the numerical solutions and tabulates numerical values, but displays an error message as I try to plot them with odeplot. The message is

Error, (in StringTools:-Remove) mapped expression must return `true' 
or `false'
 

Though, you can obtain the plot by forming a list of lists with the points by using instead of odeplot the command

plot([seq([i/10,log10(rhs(S0(i/10)[2]))], i=0..25)], color=black);
 

Afterwards, since I could not get any plot with odeplot I quit Maple and tried to start a new session, but got the error message

"The application Maple has unexpectedly quit... etc"
 

Hence I had to force-quit the whole Classic environment. This annoying bug does not happen if running the same commands under Mac OS 9.x. Hopefuly the Mac OS X native version of Maple might come soon. I write below the transcript of the Maple session (after re-executing the group of commands)

 > restart; 
 > eqMN:=(beta0,lambda0,x)->diff(M(x),x)=piecewise(x>0, 
              x^2*(exp(beta0-beta(x))+lambda0), x=0, 0); 
 
   eqMN := (beta0, lambda0, x) -> diff(M(x), x) = piecewise(0 < x, 
 
          2 
         x  (exp(beta0 - beta(x)) + lambda0), x = 0, 0) 
 
 > eqbN:=(lambda0,x)->diff(beta(x),x)=piecewise(x>0, 
               (M(x)/x^2-lambda0*x)*beta(x), x=0, 0); 
 
   eqbN := (lambda0, x) -> diff(beta(x), x) = 
 
                          /M(x)            \ 
         piecewise(0 < x, |---- - lambda0 x| beta(x), x = 0, 0) 
                          |  2             | 
                          \ x              / 
 
 > S0:=dsolve({eqMN(10^6,0,x),eqbN(0,x),M(0)=0,beta(0)=10^6}, 
              {M(x),beta(x)},type=numeric, method=lsode); 
 
                   S0 := proc(x_lsode)  ...  end proc 
 
 > seq(S0(.5*i), i=1..5); 
 
                                         -5 
   [x = .5, M(x) = .107253635455685075 10  , 
 
                                         7 
         beta(x) = .100001172170238756 10 ], [x = 1.0, 
 
                                      -5 
         M(x) = .207236310045923610 10  , 
 
                                         7 
         beta(x) = .100001321418795199 10 ], [x = 1.5, 
 
                                      -5 
         M(x) = .300759851927367088 10  , 
 
                                         7 
         beta(x) = .100001405604256631 10 ], [x = 2.0, 
 
                                      -5 
         M(x) = .391263046364007452 10  , 
 
                                         7 
         beta(x) = .100001463943739084 10 ], [x = 2.5, 
 
                                      -5 
         M(x) = .480790975386358341 10  , 
 
                                         7 
         beta(x) = .100001508190117218 10 ] 
 
 > plots[odeplot](S0,[x,log10(M(x))],0..2.5,color=black); 
Error, (in StringTools:-Remove) mapped expression must return `true' 
or `false' 
 
 > plot([seq([i/10,log10(rhs(S0(i/10)[2]))], i=0..25)], color=black);