function input to solve ODE

I am trying to write code to accept 3 arbitrary functions of time (i.e. cos, sin, t^2, etc.) and pass them to a loop that solves for an approximate solution using Euler's Method (the for loop). The error I receive is "Nonscalar arrays of function handles are not allowed; use cell arrays instead." This is the line of code with the function handle F. The code is shown here:

% solve u'(t) = F(t,u(t)) where u = [u1(t), u2(t), u3(t)]'  
% using forward euler method
% Initial conditions and setup
neqn = 3; % set a number of equations 
h=input('Enter the step size:  '); % step size will effect solution size
t=(0:h:4).';%(starting time value 0):h step size
nt = size(t,1); % size of time array
u = zeros(nt,neqn); % initialize the u vector with zeros
v=input('Enter the intial vector values of 3 components using brackets [u1(0),u2(0),u3(0)]:  ');
u(1,:)= v; % the initial u value amd the first column
v1=input('Enter the first vector fuction of time u1(t):  ','s');
v2=input('Enter the first vector fuction of time u2(t):  ', 's');
v3=input('Enter the first vector fuction of time u3(t):  ', 's');
u1 = str2func(v1);
u2 = str2func(v2);
u3 = str2func(v3);
F = @(t,u) [u1,u2,u3];  % define the function 'handle', F
% The loop to solve using Euler's Method
for i = 1:nt-1
  u(i+1,:) = u(i,:) + h*F(t(i),u(i,:)); % Euler's formula for a vector function F
end

Answer 1

[Walter Roberson]

F = @(t,u) [u1(t,u), u2(t,u), u3(t,u)];  % define the function 'handle', F

[Chris Horne]

Walter, thanks for the tip. I revised the function handle as but still there is some 'sin' and not working.

v1=input('Enter the first vector fuction of time u1(t):  ','s');
v2=input('Enter the first vector fuction of time u2(t):  ', 's');
v3=input('Enter the first vector fuction of time u3(t):  ', 's');
u1 = str2func(v1);
u2 = str2func(v2);
u3 = str2func(v3);
F = @(t,u) [u1(t,u1), u2(t,u2), u3(t,u3)];  % define the function 'handle', F
% F = str2func(['@(t,u) [',v1,',',v2,',',v3,']']);

>> Enter the step size: 0.1

Enter the intial vector values of 3 components using brackets [u1(0),u2(0),u3(0)]: [0,0,0]

Enter the first vector fuction of time u1(t): sin

Enter the first vector fuction of time u2(t): cos

Enter the first vector fuction of time u3(t): tan

Undefined function 'sin' for input arguments of type 'function_handle'.

Answer 2

[Torsten]

% solve u'(t) = F(t,u(t)) where u = [u1(t), u2(t), u3(t)]'  
% using forward euler method
% Initial conditions and setup
neqn = 3; % set a number of equations 
h=input('Enter the step size:  '); % step size will effect solution size
t=(0:h:4).';%(starting time value 0):h step size
nt = size(t,1); % size of time array
u = zeros(nt,neqn); % initialize the u vector with zeros
v=input('Enter the intial vector values of 3 components using brackets [u1(0),u2(0),u3(0)]:  ');
u(1,:)= v; % the initial u value amd the first column
v1=input('Enter the first vector fuction of time u1(t):  ','s');
v2=input('Enter the first vector fuction of time u2(t):  ','s');
v3=input('Enter the first vector fuction of time u3(t):  ','s');
F = str2func(['@(t,u) [',v1,',',v2,',',v3,']'])
% The loop to solve using Euler's Method
for i = 1:nt-1
    u(i+1,:) = u(i,:) + h*F(t(i),u(i,:)); % Euler's formula for a vector function F
end
plot(t,u)
end

[Chris Horne]

Now when I enter a function like sin(t), I get the error: "Warning: The input to STR2FUNC "sin(t)" is not a valid function name. This will generate an error in a future release.

> In eulertest2 (line 14)

[Torsten]

I suggest googling the warning to find a better solution.

But who cares about future releases ...

[Torsten]

Another way that works for me:

% solve u'(t) = F(t,u(t)) where u = [u1(t), u2(t), u3(t)]'  
% using forward euler method
% Initial conditions and setup
neqn = 3; % set a number of equations 
h=input('Enter the step size:  '); % step size will effect solution size
t=(0:h:4).';%(starting time value 0):h step size
nt = size(t,1); % size of time array
u = zeros(nt,neqn); % initialize the u vector with zeros
v=input('Enter the intial vector values of 3 components using brackets [u1(0),u2(0),u3(0)]:  ');
u(1,:)= v; % the initial u value amd the first column
v1=input('Enter the first vector fuction of time u1(t):  ','s');
v2=input('Enter the first vector fuction of time u2(t):  ','s');
v3=input('Enter the first vector fuction of time u3(t):  ','s');
F = strcat('[',v1,',',v2,',',v3,']');    
F = eval(['@(t,u)' F]);
% The loop to solve using Euler's Method
for i = 1:nt-1
    u(i+1,:) = u(i,:) + h*F(t(i),u(i,:)); % Euler's formula for a vector function F
end
plot(t,u)

[Chris Horne]

Thanks. This worked!

[Torsten]

And the other solution didn't work or only threw a warning ?

I can't test it at the moment.

[Torsten]

Just out of curiosity:

Why do you use the Euler method to integrate a function that only depends on the independent variable t ?

There are methods that are much better suited and have a higher precision:

https://en.wikipedia.org/wiki/Numerical_integration

[Chris Horne]

Thanks. Because I am learning Diff Eqs.

[Torsten]

But these are no differential equations in the usual sense.

[Chris Horne]

That's fine. Mathematics is broad and deep. Thanks for your help