Using loop instead of hardcoding

Hi everyone,

%inputs
dvdt = @(t,v) t-v;
v0 = 1;
tspan = [0 1];
% h = 0.7
h = 0.7;
[ta,va] = midpoint(dvdt,tspan,v0,h);

%% h = 0.5
h = 0.5;
[tb,vb] = midpoint(dvdt,tspan,v0,h);

%% h = 0.1
h = 0.1;    
[tc,vc] = midpoint(dvdt,tspan,v0,h);

%% h = 0.05
h = 0.05;
[td,vd] = midpoint(dvdt,tspan,v0,h)

%% MIDPOINT FUNCTION
if ~(tspan(2)>tspan(1))
    error('upper limit must be greater than lower')
end

% Create all independent values, t
%use tspan to create a vector with spacing = h;
t = [tspan(1):h:tspan(2)]';
n = length(t);
if t(end) < tspan(2)
    t(n+1) = tspan(2);
    n = n+1;
end    
% add extra t-value if needed
%check if final t-value can be achieved using the current h 
%if not, add a new t-value to the end of t
% Implement Euler's method
%use a for loop
%pre allocate the solution vector
%y = zeros(1,n)
%y(1) = y0
y = y0*ones(n,1); % 1 line
for i = 1:n-1 %stop at n-1 because dont need to calculate the deriative for final interation
    %singeline for euler's method 
    thalf = t(i) + (t(i+1)-t(i))/2;
    yhalf = y(i) + (t(i+1)-t(i))/2 * dydt(t(i),y(i));%euler's with half step
    y(i+1) = y(i) + (t(i+1)-t(i))*dydt(thalf,yhalf); %using derivative at half step  
end

QUESTION:

Instead of just typing particular h and solving each h respectively, how can I make a loop for it ?.

Thanks in advace

Answer 1

[Saumya Goel]

You can create an array for h and then iterate usign for loop according to size of the array "h".

While storing the output of the for loop you can have two arrays as "t" and "v" which can be iterated over to store the results, instead of having different variables as ta,tb,tc and so on.

For example:

N = [1 2 3];
t = zeros(1,length(N));
v = zeros(1,length(N));
for n = 1 : length(N)
  [t(n),v(n)] = val(N,n);
  
end

function [xyz,abc] = val(N,n)
    xyz = N(n);
    abc = N(n);
end