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I programmed a Nystrom Algorithm specifically for my problem:

This is the exact equation i want to solve:


And this is my algorithm

function [T U] = Nystrom(a,b,u0,h,w,v,e)
% a is the initial value
% b is the final value
% u0 is a vector with the initial conditions y(0) and y'(0)
% h is the size of every step
% w, v and e are constants.

M=(b-a)/h+2; %Steps
T=zeros(1,M+2); %Time vectors
U=zeros(2,M+2); %y and y' vector
T=a:h:b; % i use uniform steps of size h
U(:,1)=u0; %i stablish the initial conditions

U(1,2)=U(1,1)+h*U(2,1)+(h^2)/2 * (w^2-e*cos(T(1))*sin(U(1,1))-v*U(2,1));

for i=3:M

for i=1:M


The problem is, it doesn't work and i don't know why. It's throwing values bigger and bigger in every step, but solving the same problem with other methods gives different, quite smaller values.

Any idea could help. Thank you!

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