Solve MATLAB fsolve Equation: x-(r/4)*sin(pi*x)=0

[krnhseya]

I think I posted in a wrong forum...I wasn't sure which category I was supposed to post this under but here it goes...

1. Homework Statement

Find x where r varies from 0 to 4.

2. Homework Equations

x-(r/4)*sin(pi*x)=0

3. The Attempt at a Solution

The problem that I ran into with MATLAB is that when I create a sub-m file for fsolve, it requires 2 equations whereas I only have 1 equation.

function F=myfun(x,r)
F(1)=x-(r/4)*sin(pi*x);

My executable is:

var_new=[];
for r=0:0.01:4;
var=fsolve(@myfun,0.5)
var_new=[var_new var]
i=i+1;
end

I expect to get "var" variable to be a single number where my "relevant equation" is set to zero. var_new is simply creating an array for me to plot r versus var.

Thank you.

 

[krnhseya]

So 1 equation and 1 variable...Looks darn easy but I just can't figure this out and MATLAB examples that I can find (including built-in help) doesn't get me any more help...Anyone...?

 

[krnhseya]

My new attempt...

i=1;
new_x=[];
newnewx=[];

for r=0.5:0.01:4;
new_x(i)=fsolve(@myfun,[0 r]);
newnewx(i)=((r*pi)/4)*cos(pi*new_x(i));
i=i+1;
end
r=0.5:0.01:4;

plot(r,newnewx)

where the myfun is:

function F=myfun(x)
x=x(1);
r=x(2);
F(1)=x-((r/4)*sin(pi*x));

 

[bob1182006]

What you can do is define r outside of the loop, then loop through a variable i that goes from 1:length(r). Inside of the loop define the function F so that r is not a variable but a constant for each iteration.

But if you need to have the function in a separate script you can try and create a new function F2(x) = F(x,r) where r is some specific number. I don't think fsolve will just accept a multivariable function.

 

[DeeNos]

Thank you for your post. Based on the information provided, it seems like you are trying to use the fsolve function in MATLAB to solve a single equation with one variable (x) and a parameter (r). The fsolve function in MATLAB is typically used to solve systems of equations, which is why it requires two equations as input. However, it is still possible to use fsolve to solve a single equation with one variable and a parameter by modifying the input arguments.

One way to do this is to define your equation as a function of only one variable (x) and use an anonymous function to specify the parameter (r). For example, you can define your equation as follows:

myfun = @(x) x - (r/4)*sin(pi*x);

Then, you can use this function in the fsolve command as follows:

var = fsolve(myfun, 0.5);

This will give you the value of x that satisfies the equation for a given value of r. You can then use a loop to vary the value of r and solve for x at each iteration, as shown in your example code.

I hope this helps. Let me know if you have any further questions.