Backward Euler with LU Decomposition

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Vince Smith 2019-6-2

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链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/465132-backward-euler-with-lu-decomposition

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)];