Using the improved Euler (Huen) method, determine the approximate solution y (t) of the following starting problem:

Using the improved Euler (Huen) method, determine the approximate solution y (t) of the following starting problem:

dy / dt = y * e ^ 5t, y (0) = 1; t; [0, 0.5]

for time steps: h = ½; h = ¼; h = 1/8; h = 1/16; h = 1/32;

Then solve the above differential equation using the separated variables method. Compare the obtained numerical results on the graph with the exact solution y (t). Calculate the global error en for each of the time steps h and determine on this basis the order of the improved Euler (Huen) method. I have to solve it in Matlab, but I have problem with doing the script. If anyone would provide me to simple code for the solution, it would be really helpfull for me. Thank you for all the answers and tips :)

[Jan]

This forum will not solve your homework. Please post, what you have tried so far and ask a specific question.

[darova]

Show your paper

[Walter Roberson]

Torsten answered the question. It is too late to delete it now.

[Rena Berman]

(Answers Dev) Restored edit

Answer 1

[Torsten]

Untested !

function main
H = [1/2 ,1/4,1/8,1/16,1/32];
t0 = 0;
t1 = 0.5;
y0 = 1;
f = @(t,y) y*exp(5*t);
for i= 1:numel(H)
  h = H(i);
  t = (t0:h:t1).' ;
  N = numel(t);
  y = zeros(N,1);
  y(1) = y0;
  for j = 2:N
    yhelp = y(j-1) + h*f(t(j-1),y(j-1));
    y(j) = 0.5*y(j-1) + 0.5*(yhelp + h*f(t(j),yhelp));
  end
  T{i} = t;
  Y{i} = y;
end
plot(T,Y)
end

[Torsten]

@Jan: Thank you for formatting.