Backward Euler with LU Decomposition

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Vince Smith
Vince Smith on 2 Jun 2019
The code below solves forward Euler for a pendelum problem. How would I modify this code to solve with backward Euler and LU Decomposition?
length= 5;
g=9.8 ;
npoints = 5000;
dt = 0.01;
omega = zeros(npoints,1);
theta = zeros(npoints,1);
time = zeros(npoints,1);
theta(1)=0.5;
for step = 1:npoints-1
omega(step+1) = omega(step) - (g/length)*theta(step)*dt;
theta(step+1) = theta(step)+omega(step)*dt;
time(step+1) = time(step) + dt;
end
forward=[theta(end);omega(end)];

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