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I have a program for Eulers method >>

% Euler's Method for dy/dt = cost

k = 1;

y0 = 0;

npoints = 500;

dt = 0.01;

y = zeros(npoints,1); % this initializes the vector y to being all zeros

t = zeros(npoints,1);

y(1) = y0; % the initial condition

t(1) = 0.0;

for step=1:npoints-1 % loop over the timesteps

y(step+1) = y(step) + dt*k*(cos(y(step)));

t(step+1) = t(step) + dt;

end

plot(t,y,'r'); %plots the numerical solution in red

hold on; %keep the previously plotted lines

plot(t,yexact2(t)); %plots the exact solution (default plot is in blue, solid line)

The graph asymptotically approaches pi/2, and I cant think of a way to deal with this.

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# Euler's Method in MAtlab

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