Using fsolve with an interval of values

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Nick Barker
Nick Barker 2015-7-15
编辑： Nick Barker 2015-7-17
Hello:
I am having some issues with fsolve in relation to using it for equations on an interval of 0 to 6pi with an increment of pi. I have made a function file that writes the set of equations as such:
function F=eqns(x, c)
% p=x(1) and q=x(2); see Padouissis article for more information; F{1}=0 and F{2}=0
x(1) = 0:pi:6*pi;
F{1} = (x(1).^(2).*x(2).^(2).*(x(2).^(2)+x(1).^(2))+c^(2).*(x(1).^(4)+x(2).^4-6.*x(1).^(2).*x.^(2))-3*c^(4).*(x(1).^(2)-x(2).^(2))-4.*c^(6)).*sin(x(1)).*sinh(x(2))+2.*x(1).*x(2).*(-x(1).^(2).*x(2).^(2)+3.*c^(2).*(x(1).^(2)-x(2).^(2))-7.*c^(4)).*cos(x(1)).*cosh(x(2))-x(1).*x(2).*(x(1).^(4)+x(2).^(4)+2.*c^(2).*(x(2).^(2)-x(1).^(2))+2.*c^(4)).*cos(2*c);
F{2} = 2.*c.*x(1).*(3.*x(1).^(2).*x(2).^(2)-x(2).^(4)-c^(2).*(x(1).^(2)+x(2).^(2))+4.*c^(4)).*cos(x(1)).*sinh(x(2))+2.*c.*x(2).*(x(1).^(4)-3.*x(2).^(2).*x(1).^(2)-c^(2).*(x(1).^(2)+x(2).^(2))-4*c^(2)).*sin(x(1)).*cosh(x(2))+x(1).*x(2).*((x(1).^(2)+x(2).^(2)).*(x(2).^(2))-x(1).^(2)+2.*c^(2)).*sin(2*c); % code
Then use the user made function (a code that was devised by a user on the forums, you have been a great help, and it is greatly appreciated), eqns_driver:
function eqns_driver
c = input('input value c');
x0 = [2 2]; %replace with initial conditions appropriate for your purpose
result = fsolve(@(x) eqns(x, c), x0);
My ultimate goal is to make a plot with x(1) and x(2).
Thank you. I greatly appreciate it.
Edit: I apologize if my question was unclear. I am currently trying to replicate a special case of the equation systems where c = 0, and thus the values of x(1) are already given. However, I would like to make a program where c can be any real number that the user wishes to input and solve and plot for those x(1) and x(2).
The value of c is not something I am trying to solve for or plot, but only determines how the two simultaneous equations will be set up. I can provide the graph I am trying to replicate if that will help make my question clearer.

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回答（1 个）

Torsten
Torsten 2015-7-15
Use F(1,1)=... and F(2,1)=... instead of F{1}=... and F{2}=...
Furthermore, it's not clear to me which variable you want to vary.
If it's really x(1) as written, you only need one equation to calculate x(2), not two.
Best wishes
Torsten.
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Torsten
Torsten 2015-7-17
Try
function main
C=0:0.1:5;
x0=[0 ; 0];
for i=1:length(C)
c=C(i);
result = fsolve(@(x) eqns(x, c), x0);
RESULT(1,i)=result(1);
RESULT(2,i)=result(2);
x0=[result(1) ; result(2)];
end
plot(RESULT(1,:),RESULT(2,:));
function F=eqns(x, c)
F = [(x(1).^(2).*x(2).^(2).*(x(2).^(2)+x(1).^(2))+c^(2).*(x(1).^(4)+x(2).^4-6.*x(1).^(2).*x.^(2))-3*c^(4).*(x(1).^(2)-x(2).^(2))-4.*c^(6)).*sin(x(1)).*sinh(x(2))+2.*x(1).*x(2).*(-x(1).^(2).*x(2).^(2)+3.*c^(2).*(x(1).^(2)-x(2).^(2))-7.*c^(4)).*cos(x(1)).*cosh(x(2))-x(1).*x(2).*(x(1).^(4)+x(2).^(4)+2.*c^(2).*(x(2).^(2)-x(1).^(2))+2.*c^(4)).*cos(2*c);
2.*c.*x(1).*(3.*x(1).^(2).*x(2).^(2)-x(2).^(4)-c^(2).*(x(1).^(2)+x(2).^(2))+4.*c^(4)).*cos(x(1)).*sinh(x(2))+2.*c.*x(2).*(x(1).^(4)-3.*x(2).^(2).*x(1).^(2)-c^(2).*(x(1).^(2)+x(2).^(2))-4*c^(2)).*sin(x(1)).*cosh(x(2))+x(1).*x(2).*((x(1).^(2)+x(2).^(2)).*(x(2).^(2))-x(1).^(2)+2.*c^(2)).*sin(2*c)];
Best wishes
Torsten.
Nick Barker
Nick Barker 2015-7-17
Hello Torsten:
While fsolve did process it. It did not give me the graph I am trying to replicate. In fact, I got an empty graph.

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