MaplePrimes - answers and comments on Question, weird error that I don't understand

Not PDE's

Adri van der Meer — Fri, 01 Feb 2013 20:04:52 Z

These are a system of nonautonomous ODE's. I try to find a numeric solution of the IVP:

t := diff(X(x), x) = -(1-6*R(x)^(1/2))^(1/2)*x*X(x)/(X(x)*x+R(x))^(1/2), 
     diff(R(x), x) = (1-6*R(x)^(1/2))^(1/2)*x^2*X(x)/(X(x)*x+R(x))^(1/2):
init := R(0) = 0, X(0) = 100:
sol := dsolve( {t,init}, {R(x),X(x)}, type=numeric, range=0..2 ):
Warning, cannot evaluate the solution past the initial point, problem may be complex, 
initially singular or improperly set up

Indeed, "initially singular": both denominators are zero at x=0.
So I take other IV's:

init := R(1) = 0, X(1) = 100:
sol := dsolve( {t,init}, {R(x),X(x)}, type=numeric, range=1..1.05 ):
plots:-odeplot(sol, [x,R(x)], refine=50);

plots:-odeplot(sol, [x,X(x)], refine=50);

Syntax error

Preben Alsholm — Fri, 01 Feb 2013 20:07:19 Z

It should be
init:= R(0) = 0, X(0) = 100;

When using PDEtools:-Solve you need to give the variables [R(x),X(x)] as a second argument.
However, I don't know if you will have any luck with this approach.

Special handling at 0 and later.

Preben Alsholm — Fri, 01 Feb 2013 21:08:34 Z

Your system (with the unusual name of t):
t := diff(X(x), x) = -(1-6*R(x)^(1/2))^(1/2)*x*X(x)/(X(x)*x+R(x))^(1/2),
diff(R(x), x) = (1-6*R(x)^(1/2))^(1/2)*x^2*X(x)/(X(x)*x+R(x))^(1/2);
init:=R(0) = 0, X(0) = 100;
#The obvious problem at x = 0 can be handled by taking the limit for x->0. On both right hand sides we get 0.
#Another problem occurs when 1-6*sqrt(R(x)) = 0.
#So here is a revised system:
sys:=diff(X(x), x)=piecewise(x>0 and 6*sqrt(R(x))<1,rhs(t[1]),0),
diff(R(x), x)=piecewise(x>0 and 6*sqrt(R(x))<1,rhs(t[2]),0);
res:=dsolve({sys,init},[X(x),R(x)],numeric);
plots:-odeplot(res,[x,R(x)],0..0.5);
plots:-odeplot(res,[x,X(x)],0..0.5);

thx guys you have been really helpful, is

gdog — Sun, 03 Feb 2013 01:19:23 Z

thx guys you have been really helpful, is it possible to get these bot honto the same plot?

thx guys, is there a setting to allow for X(1

gdog — Sun, 03 Feb 2013 17:54:18 Z

thx guys, is there a setting to allow for X(1) to be a very large number, because when i try and plot say 10^20 it wont work?

PDEtools:-Solve just calls dsolve for ode case

Carl Love — Fri, 01 Feb 2013 22:07:31 Z

PDEtools:-Solve just passes the problem on to dsolve if it detects that they're ODEs. If dsolve is used for this problem without the numeric option, it will spend a huge amount of time and memory trying to find a symbolic solution. I didn't let it finish, as I was getting close to my memory limit.