Question

Write a function M-file my_euler.m which take 5 input values, f, t_0, y_0, dt, and t_f that specify the function to be approximated, the initial t-value, the initial condition y(t0)=y0, the step-size Δt, and the final t-value at which you want to approximate the solution y(t). Your function should:

• Use the input anonymous function f to calculate f(t,y).
• Plot the approximate solution with green "+" symbols at the points and a red line joining them up.
• Have a function output giving the numerical value of the approximate solution to y(t) at the final t-value, t_f.

By using this code, modify it. All variables inside my_euler.m the should be calculated from the input variables so that you can run the function from the Command Window.

t = zeros(1,8+1);

y = zeros(1,8+1);

t(1) = 1;

y(1) = 0;

dt = 0.25;

for k = 1:8

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

y(k+1)=y(k)+dt*f(t(k),y(k));

f = @(t,y)(2*t*exp(-1/t) +y/t^2);

end

plot(t,y,'ro-')

t(end)

y(end)

Answer 1

function yn = my_euler(f,t_0,y_0,dt,t_f)
    t=t_0:dt:t_f;
    y=zeros(1,length(t));
    y(1)=y_0;
    for i = 2:length(y)
        y(i)=y(i-1)+dt*f(t(i-1),y(i-1));
    end
    yn=y(end);
    plot(t,y,'r-+','MarkerEdgecolor','g')
end