Resolving errors with Raphson method

Hello,

I am having difficulties in writing a Raphson method using a while loop. Matlab keeps returning error: y(0): "subscripts must be either integers 1 to (2^63)-1 or logicals". I have tried to change my code several times, to try to solve this problem, but I have been unsuccesful. I am wondering if anyone has any suggestions on how to solve this problem?

[Star Strider]

The problem is that it appears that you are using C syntax in MATLAB. That will not work. You probably need to re-write the entire file in valid MATLAB code.

That aside, in MATLAB, indexing begins at 1, not 0, and subscripts (indices) need to be integers greater than 0.

[Alexander]

Thanks for the tips! It did help a lot, I was not able to identify the exact problem. It seems that my function y is not defined for any nonintegers and x = 0. Since x only numbers in the span [0, 1], it will not be defined for any value of x except 1, since y is neither defined for y(0). Any ideas why this can be? The strangest thing is that the plot function works. But if you try for example y(0.02) it will not work.

L = 1;

x = linspace(0,1,100);

y = (8*x)/(3*L) - 3*(x/L).^2 + (1/3)*(x/L).^3 - (2/3)*sin((pi*x)/L);

uy = 1/6*y;

plot(x,y)

[Dyuman Joshi]

You have to loop over the values [1 2 3 ... length(x)], right? If yes, why not use a for loop? Because you are not breaking out of the while loop if a condition is met.

Also, I don't understand why you are adding x(i) to i, in the last line of the while loop.

[Alexander]

Switched to a for loop and it works much better

Answer 1

[Star Strider]

My pleasure!

The ‘y’ assignment needs to be an anonymous function, if I understand correctly what you want to do.

That change produces this result —

L = 1;
x = linspace(0,1,100);
y = @(x) (8*x)/(3*L) - 3*(x/L).^2 + (1/3)*(x/L).^3 - (2/3)*sin((pi*x)/L);       % Anonymous Function
uy = 1/6*y(x);

figure
plot(x, y(x), 'DisplayName','y(x)')
hold on
plot(x, uy, 'DisplayName','uy(x)')
hold off
grid
xlabel('x')
ylabel('Function Values')
legend('Location','best')

See the documentation on Anonymous Functions for details. Call them as you would any other function. Similar to variables, they must be defined before they are used in the code they are implemented in.

.

[Alexander]

Thank you so much for your solution!

I got the whole code running now, I switched from a while loop to a much simpler for loop and it runs smoothly!

[Star Strider]

As always, my pleasure!

Great!