how to solve two equations

Hello

This is part of a code and I want to solve this part

thanks in advance

=========================================

clear

syms U10 U20

p=0

f =[2*U20 + sin(U20 - sin(p)) - 2*sin(p);2*U10 + sin(U10 - cos(p)) - 2*cos(p)]

s=subs(f,U10,x(1))

s1=subs(s,U20,x(2))

fun=@(x)[sin(x(2))+2*x(2); sin(x(1)-1)+2*(x(1)-1)];

fun=@(x)f;

[x,fval]=fsolve(fun,[0;0]);

U10=x(1)

U20=x(2)

[Dyuman Joshi]

It's not clear as to what you are trying to do. I am confused as to why you are using syms variable and solving with fsolve?

What is the purpose of subsitution? And you are over-writing fun

fun=@(x)[sin(x(2))+2*x(2); sin(x(1)-1)+2*(x(1)-1)];
fun=@(x)f;

[Adham Ahmed]

my friend I want solve these equations with the same variables U10 and U20 because they are part of other code

2*U20 + sin(U20)

2*U10 + sin(U10 - 1) - 2

Answer 1

[Sai]

Hi,

I understand that you are trying to solve two nonlinear equations depending on two variables.

As the equations are not clear in the data provided, let me simplify and finalize the equations to be solved.

First equation: 2*x(1) + sin(x1)

Second equation: 2*x(2) + sin(x(2)-1) - 2

Now the equations are solved using fsolve command as shown.

Following code is placed in eq_solve.m file

function f = eq_solve(x)
f(1) = 2*x(1) + sin(x(1));
f(2) = 2*x(2) + sin(x(2)-1) - 2;

Following code is placed in eq_solve_test.m file

fun = @eq_solve;
x0 = [0;0];
x = fsolve(fun,x0)

Now the eq_solve_test.m file has been run to get the values

Please refer to the fsolve documentation for future reference.

With Regards,

G. Saikumar

MathWorks Technical Support

[Adham Ahmed]

my friend I want solve these equations with the same variables U10 and U20 because they are part of other code

2*U20 + sin(U20)

2*U10 + sin(U10 - 1) - 2

Answer 2

[John D'Errico]

Note that the two equations are fully uncoupled. This means U20 appeared only in one equation. It has absolutely no impact on the other equation, and U10 has no impact on equation 1. Do you see that?

syms p U20 U10
2*U20 + sin(U20 - sin(p)) - 2*sin(p) == 0

ans = 

2*U10 + sin(U10 - cos(p)) - 2*cos(p) == 0

ans = 

the value of p does have an impact on these equations, but only in a very minor way. In fact, once you solve one of the equations, you could compute the solution to the other equation.

In this case, of course, with p==0, the problem becomes even simpler. The first equation reduces to

fun = @(U20) 2*U20 + sin(U20);
fplot(fun)
yline(0)

That problem provably has a solution only at U20==0, and the solution will be unique for real values of U20. We don't even need to use a tool like solve or fzero or fsolve to solve the problem.

Similarly, when p==0, the second equation reduces to

2*(U10-1) + sin(U10 - 1) == 0

My point is, this equation is identically the same as the first equation, but with a transformation appied

U20 == U10 -1

So if we have U20==0 as a solution to the first equation, then trivially we know that U10==1.

If p weret o take on some other values, then the problem is no more difficult, since your system of two equations is not only an uncoupled system, but once you solve the problem once, you can solve the second problem directly. There are no rootfinders ever needed in the end.

[Adham Ahmed]

my friend I want solve these equations with the same variables U10 and U20 because they are part of other code

2*U20 + sin(U20)

2*U10 + sin(U10 - 1) - 2

[Torsten]

What about U10 = 1, U20 = 0 ?

[Adham Ahmed]

I Know that is the answer but I need a small code to do it with the same sympolic variables

thank you

[Torsten]

syms U10 U20 
[U10 U20] = vpasolve([2*U10 + sin(U10 - 1) - 2==0,2*U20 + sin(U20)==0],[U10 U20])

U10 = 

1.0

U20 = 

0

[Adham Ahmed]

Thank you

can you help me to run this code ?

syms U10 U20

Afk=[f1,f2]

Afk=[2*U10 + sin(U10 - 1) - 2,2*U20 + sin(U20)]

[U10 U20] = vpasolve([f1==0,f2==0],[U10 U20])

[Torsten]

syms U10 U20 
Afk=[2*U10 + sin(U10 - 1) - 2,2*U20 + sin(U20)]

Afk = 

[U10 U20] = vpasolve(Afk)

U10 = 

1.0

U20 = 

0