Am I passing a function through correctly?

I was trying to to write a function that uses the Euler method to calculate the nth iteration solution of a function y. As inputs, it takes a function handle passed through in terms of variables (t, y). Then it solves for the iteration number n, based on the desired final t value, Tf, t0, and the time step dt, using the equation tn=t0+n*dt =>Tf=t0+n*dt. Then outputs the vectors t and y of t and y values generated after each iteration so, starting with t0 and y0 and going up to the values (Tf, yn). I was wondering if the function would return every set of (t, y) vectors for each iteration in an array, if I allocated the space prior to the loop, or if I would need to simply print (tn, yn) at the end of the loop itself. I thought I would need to create an array in order to return every (t, y) vector created, instead of just the last one:

function [t,y]=eulerMethod(f3, dt, Tf, t0, y0)
syms n;
syms tn;
syms yn;
Tf=t0+n*dt;
S1=solve(Tf,n);
nf=round(S1);
yp=y0;
tp=t0;
nf=nf-1;
for n=0:nf
    tn=t0+n*dt;
    f3p=subs(f3,[t,y],[tn,yp]);
    yn=yp+dt*f3p;
    yp=yn;
end
syms t;
syms y;
t=tn;
y=yn;
return 

Also, I was wondering if I passed the arbitrary function f3, correctly, as follows:

f3=@(t,y) %(write fct here);
eulerMethod(f3, dt, Tf, t0, y0)

Thanks!

[Jan]

This is very confusing. Why do you use symbolic expressions for such easy numerical tasks?

Tf = t0 + n * dt;
S1 = solve(Tf,n);

What about:

n = (Tf - t0) / dt;  % Without symbolic maths

This is obscure although:

f3p=subs(f3,[t,y],[tn,yp]);

Are you sure that you do not want to use the numerical Euler method for a numerical integration? Then:

f3p = f3(t, y);

would be easier and clear.

[Ragini Ravichandren]

Got it. I was wondering whether I had originally had the following function:

function [t,y]=eulerMethod(f3, dt, Tf, t0, y0)

syms n;

n=(Tf-t0)/dt;

nf=round(n,1);

yp=y0;

for n=0:nf

tp=t0+n*dt;

f3p=f3(tp,yp);

yn=yp+dt*f3p;

yp=yn;

end

t=tn;

y=yp;

However, I couldn't really get t and y to return as outputs at the end after getting through the loop and setting them equal to yp, and tn.

[Jan]

It is still unclear, why you want to use sym at all. The Euler method is a numerical method for an integration.

Your code looks confusing. Providing "Tf" and "t0", the symbolic calculation of the number of steps, renaming y0 to yp, yn to yp, yp to y is strange also. Finally it is still not clear to me, what this means: "Euler method to calculate the nth iteration solution of a function y." I do not know, what an "n.th iteration solution" is. Here the function is not "y" also.

Usually Euler methods looks like this:

function [t, y] = eulerMethod(fcn, t0, tf, dt, y0)
t       = t0:dt:tf   % Time steps
n       = numel(t);  % or: n = floor((tf - t0) / dt);  % Number of steps
y       = zeros(numel(y0), n);    % Pre-allocate the output
y(:, 1) = y0;        % Start at initial value
for k = 2:n
    dy      = fcn(t(k - 1), y(:, k - 1));
    y(:, k) = y(:, k - 1) + dt * dy;
end
end