How can we solve time dependent non linear equations?

Consider the time dependent nonlinear equaionbs as follows;

a=0.2; b=2.92; c=4; %%Constant

f1(x(t),y(t),z(t)) = -a*a - b*b + y(t)*y(t) + z(t)*z(t);

f2(x(t),y(t),z(t)) = -b*b - c*c - x(t)*x(t) + z(t)*z(t);

f3(x(t),y(t),z(t)) = -1- x(t)*x(t) + y(t)*y(t);

where time 't' is varying from 0 to 1000/infinity....

NOTE:

f1, f2 and f3 are only function of variables x(t) ,y(t) and z(t) respectively. They are not representing derivative with respect to time 't'.

How can we sove them and how can plot them with respect to time?

Please help me regarding this issue.

Thanking you!

[Fabio Freschi]

I don't see the time dependance of your equations

[Shadab Ali]

So how can i plot '(f1(x(t),y(t),z(t))' over time?

Like x-axis represent 't' and y-axis represent 'f1(x(t),y(t),z(t))' . Similarly for 'f2(x(t),y(t),z(t))' and 'f3(x(t),y(t),z(t))'.

[Shadab Ali]

Thanking for your response.

These are the equations to solve.

choose some initial condidtion in such a manner.

(z_1(0),z_2(0),z_3(0),z_4(0))=(0, 1, 0.5, 0)

with parameter values

a=0.9; b=0.2; c=1.5; d=1; k=0.05;

Finally, the output of the equations M1, M2, M3 and M4.

I hope now you can easily understand the problem..

Thans!

[Torsten]

You didn't specify the time-dependent functions for M1, M2, M3 and M4. Further, z4 is missing in your set of equations.

Answer 1

[Torsten]

Use "fsolve" for each value of t separately for your three equations from above.

You may use the solution of time t as initial guess for time t+1.

Answer 2

[Sam Chak]

Hi @Shadab Ali

Do you expect complex-valued solutions?

x0        = [3i 3i 4];  
% there are 7 other solutions
% x0      = [ 3i  3i -4];
% x0      = [ 3i -3i  4];
% x0      = [ 3i -3i -4];
% x0      = [-3i  3i  4];
% x0      = [-3i  3i -4];
% x0      = [-3i -3i  4];
% x0      = [-3i -3i -4];
[x, fval] = fsolve(@fun, x0)

Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.

x = 
   0.0000 + 2.9120i   0.0000 + 2.7350i   4.0058 + 0.0000i

fval = 
   1.0e-09 *

  -0.6226 + 0.0022i   0.0001 + 0.0000i  -0.6225 + 0.0011i

function f = fun(x)
    % Constants
    a    = 0.2;
    b    = 2.92;
    c    = 4;
    % Equations
    f(1) = - a*a - b*b + x(2)*x(2) + x(3)*x(3);
    f(2) = - b*b - c*c - x(1)*x(1) + x(3)*x(3);
    f(3) =         - 1 - x(1)*x(1) + x(2)*x(2);
end

[Shadab Ali]

Thank you for your response.

No, I am not looking for complex solutions.

Thanks!

you can look again, these are the equations to solve.

choose some initial condidtion in such a manner.

(z_1(0),z_2(0),z_3(0),z_4(0))=(0, 1, 0.5, 0)

with parameter values

a=0.9; b=0.2; c=1.5; d=1; k=0.05;

Finally, the output of the equations M1, M2, M3 and M4.

I hope now you can easily understand the problem..

Thanks!

[Sam Chak]

Feel like I'm seeing the Differential Algebraic Equations (DAEs). Can you verify that?

[Shadab Ali]

Thanks!

I have solve these equation.