My Euler Method Error

Question:

Consider the initial value problem: dy/dt= e−t − 3y, y(−1) = 0.

Part a: Use the MATLAB program myeuler.m from Chapter 8 to compute the Euler Method approximation to y(t) with step size h = 0.5 and n = 4 steps. The program will generate a list of ordered pairs (ti, yi). Use plot to graph the piecewise linear function connecting the points (ti, yi). Repeat with h = 0.2 and n = 10.

Code:

f = @(t,y) exp(-t)-3*y;

[t, y] = myeuler(f,-1,0,1,4);
plot(t,y)

[t, y] = myeuler(f,-1,0,1,10)
plot(t,y)

[James Tursa]

You need to show us the myeuler.m code so we know what the arguments are supposed to be.

[Bob]

Here:

function [t, y] = myeuler(f, tinit, yinit, b, n)

%MYEULER Euler approximation for initial value problem,

% dy/dt = f(t, y), y(tinit) = yinit.

% Approximations y(1),..., y(n + 1) are calculated at

% the n + 1 points t(1),..., t(n + 1) in the interval

% [tinit, b]. The right-hand side of the differential

% equation is defined as an anonymous function f.

% Calculation of h from tinit, b, and n.

h = (b - tinit)/n;

% Initialize t and y as length n + 1 column vectors.

t = zeros(n + 1, 1);

y = zeros(n + 1, 1);

% Calculation of points t(i) and the corresponding

% approximate values y(i) from the Euler Method formula.

t(1) = tinit;

y(1) = yinit;

for i = 1:n

t(i + 1) = t(i) + h;

y(i + 1) = y(i) + h*f(t(i), y(i));

end

[Walter Roberson]

What difficulty are you encountering? You did not ask a question.

http://www.mathworks.com/matlabcentral/answers/6200-tutorial-how-to-ask-a-question-on-answers-and-get-a-fast-answer

[Bob]

I keep getting an error:

Error in Project_2 (line 94) [t, y] = myeuler(f,-1,0,1,4);

[Bob]

Need help with this asap!

Thanks

Answer 1

[Walter Roberson]

Your code executes without error when I try it without change.

Make sure that the code you posted for myeuler is saved in myeuler.m and that the directory it is saved in is on your MATLAB path (for example if you are cd'd to the same directory)

[Bob]

Could you please post a screenshot to how you are ruining the code because I am still getting an error for this code:

f = @(t,y) exp(-t)-3*y;
[t, y] = myeuler(f,-1,0,1,4);
plot(t,y)
[t, y] = myeuler(f,-1,0,1,10)
plot(t,y)

or past the code that you entered.

[Walter Roberson]

>> f = @(t,y) exp(-t)-3*y;
[t, y] = myeuler(f,-1,0,1,4);
plot(t,y)
[t, y] = myeuler(f,-1,0,1,10)
plot(t,y)

t =

                          -1
                        -0.8
                        -0.6
                        -0.4
                        -0.2
       -5.55111512312578e-17
                         0.2
                         0.4
                         0.6
                         0.8
                           1

y =

                           0
           0.543656365691809
           0.662570731975217
           0.629452052868189
            0.55014576067553
           0.464338855902246
           0.385735542360898
           0.318040367559956
            0.26128015623111
           0.214274389711249
           0.175575548707944

>> dbtype myeuler.m

1       function [t, y] = myeuler(f, tinit, yinit, b, n)
2       
3       %MYEULER Euler approximation for initial value problem,
4       
5       % dy/dt = f(t, y), y(tinit) = yinit.
6       
7       % Approximations y(1),..., y(n + 1) are calculated at
8       
9       % the n + 1 points t(1),..., t(n + 1) in the interval
10      
11      % [tinit, b]. The right-hand side of the differential
12      
13      % equation is defined as an anonymous function f.
14      
15      % Calculation of h from tinit, b, and n.
16      
17      h = (b - tinit)/n;
18      
19      % Initialize t and y as length n + 1 column vectors.
20      
21      t = zeros(n + 1, 1);
22      
23      y = zeros(n + 1, 1);
24      
25      % Calculation of points t(i) and the corresponding
26      
27      % approximate values y(i) from the Euler Method formula.
28      
29      t(1) = tinit;
30      
31      y(1) = yinit;
32      
33      for i = 1:n
34      
35      t(i + 1) = t(i) + h;
36      
37      y(i + 1) = y(i) + h*f(t(i), y(i));
38      
39      end

[Walter Roberson]

Literally no changes to your code. Note even deleting extra spaces.

You need to post the exact error message -- everything that shows up in red. And check

which -all myeuler

[Bob]

Now I am getting this:

Maximum recursion limit of 500 reached. Use set(0,'RecursionLimit',N) to change the limit. Be aware that exceeding your available stack space can crash MATLAB and/or your computer.

[Bob]

What is which -all myeuler? Should I have that somewhere in the code?