How does one write a code for the IVP of y(0) = 0? The program won't accept the following. Also, can someone check my syntax for the equations I've entered? Thanks!
function ystar = Eulermethod201(n) a=0; b=5; h=(b-a)/n; t=0:h:5;%Initialize time variable
clear ystar;%wipe out old variable
ystar(0)=0;%Initial condition (same for approximation)
for i=0:length(t), %Set up "for" loop
%Calculate the derivative
k1=(-0.5*exp(t(i)/2)*sin(5*t(i))+5*exp(t(i)/2)*cos(5*t(i))-ystar(i)); ystar(i+1)=ystar(i)+h*k1;%Estimate new value of y
end %Exact solution
y=(exp(t/2))*(sin(5*t)); %Error calculation
percent_error=100*abs(y-ystar)./y; disp(percent_error); %Plot approximate and exact solutions
plot(t,ystar,'b--',t,y,'r-',t,percent_error,'g'); legend('Approximate','Exact','Error'); title('Euler Approximation n=50'); xlabel('Time'); ylabel('y*(t), y(t)');
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