Newton Raphson method problem when iterating a variable

Question

I need help with a problem. I written a program to calculate the value of a function using the Newton Raphson method. However, the function also has a variable i would like to iterate over, V. The program runs fine until the second iteration of the outer for loop, then the inner for loop will not run further once it reaches the Newton Raphson function. If someone has any ideas of what is wrong, I would greatly appreciate it. The error i get is: Warning: Solution does not exist because the system is inconsistent.

The code is below for detail.


for V = 1:50;

syms x;

f(V)= Il-x-Is.*(exp((q.*(V+x.*Rs))./(1000.*y.*K.*T))-1)-((V+x.*Rs)./Rsh); 

g(V)=diff(f(V)); 

x0 = 0;

i = 1;

for i=1:10

        f0=vpa(subs(f,x,x0)); 

        f0_der=vpa(subs(g,x,x0)); 

        y=x0-f0/f0_der; % Newton Raphson

        x0=y;
end
end

Why are you using symbolic math for this, since you're only getting an approximation anyway, why not use numerical variables? — David
I haven't really consider any other option. Would you know how I could approach a numerical program for this? — user11946635
Try fzero. Or use anonymous functions for f and g you you can do f(x0). — David
I'm not really getting anywhere with fzero and anonymous functions... Do you have any concrete examples on how I could implement it? — user11946635
The irony is, you've not given us a concrete example which you want to solve... please provide a minimal reproducible example with expected outputs for given inputs. — Wolfie

David David · Accepted Answer · 2019-11-12T23:01:50

Assuming you have a function defined like

func = @(x,V) V+x+exp(x);

There are plenty of options that avoid expensive symbolic calculations.

Firstly, making a vector of values of x0 using fzero and a for loop:

for V = 1:50
    x0(V) = fzero(@(x) func(x,V),0);
end

Secondly, the same thing again but written as an anonymous function, so you can call x0(1.5) or x0(1:50):

x0 = @(V) arrayfun(@(s) fzero(@(x) func(x,s),0),V);

Finally, if you want to use ten steps of Newton's method and calculate the derivative symbolically (although this is not a great method),

syms y Vsym
g = matlabFunction(diff(func(y,Vsym),y),'Vars',[y Vsym]);

for V = 1:50
    x0(V) = 0;
    for i = 1:10
        x0(V) = x0(V)-func(x0(V),V)/g(x0(V),V); % Newton Raphson
    end
end

Which at least will be more efficient in the loops because it's just using anonymous functions.

Newton Raphson method problem when iterating a variable

1 Answers