Re: Solving functional nonlinear equation

[Thomas Shores]

Disregard my last post.  I misread the problem.  However, I'm a bit puzzled by the delay. This file, test.m

tic;
x=linspace(.1,1,160); y=x; [xx,yy]=meshgrid(x,y);
for a = [1.1,1.2,1.5,2]
  b=1/a;zz=-b*(xx.*yy).^(b-1)+xx.^(b-1)+yy.^(b-1);
  figure; surf(xx,yy,zz);shading interp;fflush(1);

end
toc;

gave this result on my system (Octave 3.2.3, gnuplot4.2), and of course produced the plots:

octave:1> test
Elapsed time is 1.49368 seconds.
octave:2>




On 12/28/2009 02:55 PM, Thomas Shores wrote:

If your objective is to do some plotting of f(x,y) in the xy-domain, read the comments that followed your post.  If it is to solve the equation, do a bit of formal algebra:  you say that a is a positive parameter.  Make the substitution b=1/a.  If you want to avoid complex variables, restrict the domain to x, y>=0.  If y=0, than any choice of a,x will solve the equation.  If y>0, cancel y from the equation to obtain b*x^(b-1) - 1=0. Thus y is irrelevant.  Now if you want a plot in xb-domain, follow Chang's suggestions along the lines of

x=linspace(.1,1,20); b=x; [xx,bb]=meshgrid(x,b);
surf(xx,bb, bb.*xx.^(bb-1) - 1)



On 12/27/2009 06:35 AM, Dorian wrote:

Hi  all,

How do I solve  the following functional nonlinear equation using octave

f(x,y)= (-1/a^2)*(x*y)^(1/a-1)+(1/a)*x^(1/a-1)+(1/a)*y^(1/a-1) =0

where  "a"  is positive parameter. 

If there is a way to plot  f(x,y) for different values of "a"
it will be very appreciated.

Thanking you in advance

Dorian

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