The straightforward approach

Preben Alsholm — Thu, 13 Sep 2012 10:46:48 Z

eq1:=diff(f(eta),eta,eta,eta)+f(eta)*diff(f(eta),eta,eta)+beta*(1-diff(f(eta),eta)^2)=0;
eq2:=diff(theta(eta), eta, eta)+pr*f(eta)*(diff(theta(eta), eta))+pr*Ec*(diff(f(eta), eta, eta))^2
+(2-beta)*pr*Q*theta(eta) = 0;
bc:=theta(9)=0,D(theta)(0)=-Nc*(1-theta(0)),f(0)=1,D(f)(0)=lambda,D(f)(9)=1;
Para:={beta=1,Ec=0.5,Q=-0.5,Nc=5,pr=3};

#The approach is straightforward in the sense that it just hands dsolve the boundary value problem: We don't do the shooting or whatever method is used. The 'parameters' option is only available for IVPs, so we make a procedure, which for given lambda returns -D(theta)(0):

mTp0:=proc(lambda1) local res,T1;
   if not type(lambda1,numeric) then return 'procname(_passed)' end if;
   res:=dsolve(eval({eq1,eq2,bc},Para union {lambda=lambda1}),numeric,output=listprocedure);
   T1:=subs(res,diff(theta(eta),eta));
   -T1(0)
end proc;
plot(mTp0(lambda),lambda=-2..2);

But experimenting with different ranges for lambda you will notice jumps from one to another of the multiple solutions we discussed in your earlier postings.

Disconnect in a curve??

J4James — Thu, 11 Oct 2012 14:06:23 Z

I adopted the approach suggested in an earlier post (http://www.mapleprimes.com

/questions/137320-Plotting-A-System-Of-Ode) for the known results,

but some part of curve is missing.

The output I got is

and the known results are

I increased the Digit, numpoints and also went for high grid size but no luck.

I thought maybe some one would like to have a look and will help me out.

Thanks

paraplot.mw

MaplePrimes - answers and comments on Question, plotting a system of ode?

The straightforward approach

Disconnect in a curve??