Help with Euler's method?
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Consider the initial Value Problem: dy/dt=y(2-ty), y(0)=1 Use Euler's method to determine the approximate values of the solution at t=1,1.5,2,2.5 with grid sizes a)h=0.01, b)h=0.05, c)h=0.10. List results in Tabular form.
So i been trying to work on this for a while but having a lot of trouble. Any help will be greatly appreciated. Here's what I have so far:
function dy = f(t,y)
dy=(2*y)-(t*(y^2));
t0=0;
y0=1;
t1=1;
tf=2.5;
n=150
h=(tf-t1)/n
t=t1;
y=y0;
T=t;
Y=y;
for i = 1 : n % for i = 1 to n do
k = f(x,y); % the left-hand slope
y = y + h*k; % Euler step to update y
x = x + h; % update x
X = [X; x]; % adjoin new x-value
Y = [Y; y]; % adjoin new y-value
end
[X,Y]
[X(n-120), Y(n-120)]
[X(n-135), Y(n-135)]
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