Styjun

My technique of making a vector out of "column" variables in a table only works part of the time. What is different about K1 from index in the following code? I am debugging a numerical method and I need the columns index, X, K1, K2, K, Y. All works fine until I add K1, K2, and K? How to do?

MM

What is needed is to properly initalize K1, k1, K2, k2, K, and k.
Corrected code is below.

FUNCTION CODE:

function [index,X,K1,K2,K,Y] = impeulerT(x,y,x1,n)
% modified version of Improved Euler method found in
% Elementary Differential Equations by Edwards and Penney 
X=x; % initial x
Y=y; % initial y
x1 = x1; % final x
n = n; % number of subintervals
h = (x1-x)/n; % step size
index = 0; % initialize index
k1=0; K1=k1; % initialize k1
k2=0; K2=k2; % initialize k2
k=0; K=k; % initialize k
for i=1:n; % begin loop
k1=f(x,y); % first slope
k2=f(x+h,y+h*k1); % second slope
k=(k1+k2)/2; % average slope
x=x+h; % new x
y=y+h*k; % new y
X=[X;x]; % update x-column 
Y=[Y;y]; % update y-column
index = [index;i]; % update index-column
K1=[K1;k1]; % update K1 column
K2=[K2;k2]; % update K2 column
K= [K;k]; % update K column
end % end loop
ImprovedEulerTable=table(index,X,K1,K2,K,Y)
clear
end

CALL CODE:

[index,X,K1,K2,K,Y] = impeulerT(0,1,1,10);

LOG:

Output argument "index" (and maybe others) not
assigned during call to "impeulerT".

You are clearing your variables before you can return them. The error you receive can be explained here.

To fix your code, just simply remove or comment the clear statement after you create your table:

function [index,X,K1,K2,K,Y] = impeulerT(x,y,x1,n)
% modified version of Improved Euler method found in
% Elementary Differential Equations by Edwards and Penney 
 X=x; % initial x
 Y=y; % initial y
 x1 = x1; % final x
 n = n; % number of subintervals
 h = (x1-x)/n; % step size
 index = 0; % initialize index
 k1=0; K1=k1; % initialize k1
 k2=0; K2=k2; % initialize k2
 k=0; K=k; % initialize k
 for i=1:n; % begin loop
 k1=(x/y); % first slope
 k2=(x+h)/(y+h*k1); % second slope
 k=(k1+k2)/2; % average slope
 x=x+h; % new x
 y=y+h*k; % new y
 X=[X;x]; % update x-column 
 Y=[Y;y]; % update y-column
 index = [index;i]; % update index-column
 K1=[K1;k1]; % update K1 column
 K2=[K2;k2]; % update K2 column
 K= [K;k]; % update K column
 end % end loop
 ImprovedEulerTable=table(index,X,K1,K2,K,Y);
end

In general, you don't have to worry about clearing your variables inside a called function, since those variables only stay within that function's workspace. The only variables that change are the ones that are returned. Read more here on how functions work with workspaces.