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Re: Solving functional nonlinear equation

From: Thomas Shores
Subject: Re: Solving functional nonlinear equation
Date: Mon, 28 Dec 2009 14:55:11 -0600
User-agent: Mozilla/5.0 (X11; U; Linux x86_64; en-US; rv: Gecko/20091014 Fedora/3.0-2.8.b4.fc11 Thunderbird/3.0b4

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


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