How can I replace symbolic variables to solve a nonlinear system using fsolve

I am working on a system of nonlinear equations, for example:

3*u1^2 + 2*u2 - 5 = 0;

4*u1 - 3*u2^3 + 10 = 0;

where u1 and u2 are symbolic variables. I'm having much difficulties replacing u1 and u2 with x(1) and x(2) in @fun, suitable for fsolve:

 x = fsolve(fun,x0,options)

The problem is that the system of equations (and number of variables) is too large to do this manually ... Is anyone aware of an elegant/automatic solution?

Answer 1

[Azzi Abdelmalek]

1 first writte this function and save it "answerf90"

 function y=answerf90(u)
 y(1)=3*u(1)^2 + 2*u(2) - 5 ;
 y(2)=4*u(1) - 3*u(2)^3 + 10 ;

2 second

fsolve(@answerf90,[0;0])  % [0;0] your initials conditions

[Marko85]

Thank you for the answer; however, your solution does not involve symbolic variables.

[Azzi Abdelmalek]

you don't need symbolic variable

[Azzi Abdelmalek]

if a sytem is too large to writte it manualy you can writte it by using string functions

[Marko85]

In my case, system of equations comes from a system of integral equations, solved using Gauss quadrature.

The output of this integration is a large system of nonlinear algebraic equations, written in terms of symbolic variables. This system needs to be transformed in order to suit the fsolve function.

[Sumit Yelpale]

Did you find the answer? i too am facing with the same problem. Please help me

Answer 2

[Walter Roberson]

Consider using matlabFunction() to transform the symbolic expression into a function handle that can be passed to fsolve().

To handle the assignment of the vector x into other variable names, use a small routine,

function result = split_and_call( fh, x )
  xcell = num2cell(x);
  result = fh( xcell{:} );
end

[annona]

If I can ask about your answer,How to call this function?

 'fh' is the output of the 'matlabFunction' and 'x' is what ?? Is it the initial guess for 'fsolve'?

Answer 3

[Star Strider]

Starting with:

        Eqn1 = 3*u1^2 + 2*u2 - 5 == 0

        Eqn2 = 4*u1 - 3*u2^3 + 10 == 0

If you simply want the numeric solutions, this works:

        [u1, u2] = solve(Eqn1, Eqn2)

Continuing on, replacing u1 and u2 with x(1) and x(2) is fairly straightforward:

        Eqn1 = subs(Eqn1, {'u1','u2'}, {'x(1)','x(2)'})

yields:

Eqn1 =

2*x(2) + 3*x(1)^2 - 5 == 0

and

        Eqn2 = subs(Eqn2, {'u1','u2'}, {'x(1)','x(2)'})

yields:

Eqn2 =

4*x(1) - 3*x(2)^3 + 10 == 0

For some reason I can't figure out, I can't make these work:

        Eqn1m = matlabFunction(3*u1^2 + 2*u2 - 5)

        Eqn2m = matlabFunction(4*u1 - 3*u2^3 + 10)

even though matlabFunction works with other equations and variables, and these work without problems:

        Eqn1m = matlabFunction(3*x1^2 + 2*x2 - 5)

Eqn1m = 

      @(x1,x2)x2.*2.0+x1.^2.*3.0-5.0

and

        Eqn2m = matlabFunction(4*x1 - 3*x2^3 + 10)

Eqn2m =

    @(x1,x2)x1.*4.0-x2.^3.*3.0+1.0e1

However matlabFunction won't preserve the substitutions for x(1) and x(2), so you need to vectorize and then create your own anonynous functions:

        Eqn1v = vectorize(Eqn1)

Eqn1v =

2.*x(2) + 3.*x(1).^2 - 5 == 0

        Eqn2v = vectorize(Eqn2)

Eqn2v =

4.*x(1) - 3.*x(2).^3 + 10 == 0

however you're going to have to change them a bit if you want to use them with fsolve.

NOTE: I have no idea why matlabFunction doesn't like u1 and u2 as variables. I obviously declared them in my syms statement and they work everywhere else in the code, just not in matlabFunction. Weird.

Answer 4

[Marko85]

Thanks for the effort! I used:

x0 = ones(n_unkn, 1);

options = optimset('Display', 'iter');

[x fval] = fsolve(@my_fun, x0, options, virt);

function F = my_fun(x)

for i = 1:n_unkn

    eqn{i} = subs(eqn{i}, {'u', 'v', etc.}, {x(1), x(2), etc.})

end

F = [eqn{1};eqn{2}; etc.];

end

ps; a accepted a wrong answer ... (im new here) - sorry

[omnia]

If I can ask, how you get your equations in the function 'my_fun'. Yhey are only written to the main programm.

[yanyan li]

how you get your equations in the function 'my_fun'.