Error in naming function handles

Hi all,

I am writting a Runge Kutta for a time varying system of ODEs, but bumped into an error of indexing. I think the problem comes from how I type the function handle but i have no idea how to fix it.

Any clue?

Thanks!

here is the error:

Error using sym/subsasgn (line 961)

Invalid indexing or function definition. Indexing must follow MATLAB indexing. Function arguments must be

symbolic variables, and function body must be sym expression.

and here is my code:

%define function handles
fx1= @(t, x1, x2) ((-t)/(1+t^2))*x1 + x2
fx2 = @(t, x1, x2) (((-4)*t)/(1+t^2))*x2

%deine initial condition
t(1) = 0
x1(1) = 0;
x2(1) = 1;

%define step size
h = 0.1
tfinal= 5
N= ceil(tfinal/h)

%make a loop
for i = 1:N
    t(i+1)= t(i)+h; %time update
    
    k1x1= fx1(t(i), x1(i), x2(i));
    k1x2= fx2(t(i), x1(i), x2(i));
    
    k2x1= fx1(t(i)+h/2, x1(i)+h/2*k1x1, x2(i)+h/2*k1x2);
    k2x2= fx2(t(i)+h/2, x1(i)+h/2*k1x1, x2(i)+h/2*k1x2);
    
    k3x1= fx1(t(i)+h/2, x1(i)+h/2*k2x1, x2(i)+h/2*k2x2);
    k3x2= fx2(t(i)+h/2, x1(i)+h/2*k2x1, x2(i)+h/2*k2x2);
    
    k4x1= fx1(t(i)+h, x1(i)+h*k3x1, x2(i)*k3x2);
    k4x2= fx2(t(i)+h, x1(i)+h*k3x1, x2(i)*k3x2);
    
    %updating the function
    x1(i+1) = x1(i) + (h/6)* (k1x1 + 2*k2x1 + 2*k3x1 + k4x1);
    x2(i+1) = x2(i) + (h/6)* (k1x2 + 2*k2x2 + 2*k3x2 + k4x2);
    
    
    
end


%plotting the solution
plot(t,x1)
hold on
plot(t,x2)
xlabel('time')
ylabel('values')
legend('x1','x2')

Answer 1

[David Hill]

Code works just fine as stand alone. Did you previously use/assign any of your variables (t,x1,x2) as symbolic? I could not find anything wrong with your code and I pasted into matlab and ran it without error.

k2x1= fx1(t(i)+h/2, x1(i)+h/2*k1x1, x2(i)+h/2*k1x2);%Do you mean h/2/k1x2 or what you have? I would normally write h*k1x2/2 or add () to be less confusing.

[Walter Roberson]

One of t, x1, or x2 was previously a symbolic function, I can tell.

[Xingda Chen]

Hi David,

I added syms t, x1,x2 and it ran. Idk why I need it but it worked....

[Xingda Chen]

#Walter Roberson, Yes, i typed syms x1 x2 before and earsed it.

[Walter Roberson]

That code could have problems if t, x1, or x2 were defined before the code ran, including if they were defined as symbolic. You should be using

t = zeros(1, N+1);
x1 = zeros(1, N+1);
x2 = zeros(1, N+1);