How do I alter myEuler.m to calculate M and plot the solution?

Hi, I am trying to complete a Euler's approximation problem:

How do I calculate M and plot the solution?

h=1 for the IVP: y'=0.1y over [0,5] with y(0)=1000. Given the script:

function [ E] = MyEuler(f,a,b,ya,M) %Input: f is the function entered as a string 'f', see myfunc.m % a left endpoint % b right endpoint % ya initial condition y(a)=y_0 % M number of partitions, M+1 number of points %Output: E solution {t,y(t)}

h=(b-a)/M; T=zeros(1,M+1); Y=zeros(1,M+1);

T=a:h:b; Y(1)=ya;

for j=1:M Y(j+1)=Y(j) + h*feval(f,T(j),Y(j)) end

E=[T' Y'] plot(T,Y,'r:')

end

Answer 1

[Geoff Hayes]

Summer - if you want the script to calculate M rather than passing it in as a variable, then you will have to replace it with the step size h and just rearrange the calculation for h to

 M = ceil((b-a)/h);

In your case, with the step size of h equal to 1, a equal to 0, and b equal to 5, then M would become 5. (You may want to reconsider renaming this variable from M to n because that seems to be more common in the literature.)

Your call to plot seems correct, so I don't think that there is anything to change there. Putting all the above together would give the following

 function [E] = MyEuler(f,a,b,ya,h) 

    n=(b-a)/h; 

    T=linspace(a,b,n+1);
    Y=zeros(1,n+1);

    Y(1)=ya;

    for k=1:n 
        Y(k+1)=Y(k) + h*feval(f,T(k),Y(k));
    end

    E=[T' Y'] ;
    plot(T,Y,'r:');

 end

Note that I replaced the index j with k since both i and j are also used representations of the imaginary number (so it is good practice to avoid using either as indices in loops).

Note also the use of linspace which will create a vector of n+1 linearly spaced numbers from a to b.