Why am I am facing this error "Index in position 1 is invalid. Array indices must be positive integers or logical values."

I am trying to solve the 2 ODE using RK2 method and i require 2 iterations but when i try to solve for the 2nd iteration, it wont work but the first iteration is ok.

clc
y1= @(t,y,z) -exp(-t).*y^2  %Write your f(x,t) function, where dy/dt=f(x,t)
y2 = @(t,y,z) y.^2 -0.1*exp(-t).*z
t0= 0; %initial value of t(0) 
y0= 1; %initial value of y(0)
z0 = 0;
h= 0.5; %step size
%Formula: k1=h*f(x0,y0);  k2=h*f(x0+h,y0+k1); y1=y0+(k1+k2)/2;     
for i=1:2
    k1=h*y1(t0,y0,z0);
    L1 = h*y2(t0,y0,z0);
    t1=t0+h; 
    k2=h*y1(t1,y0+k1,z0+L1);
    L2 = h*y2(t1,y0+k1,z0+L1);
    y1=y0+(k1+k2)/2;
    y2=z0+(L1+L2)/2;
    t0=t1;
    y0=y1;
    z0=y2;
end
y1 %ans
y2
t1

[Jing Kai Wong]

Thanks all! I realised the mistake.

Answer 1

[Walter Roberson]

y1= @(t,y,z) -exp(-t).*y^2  %Write your f(x,t) function, where dy/dt=f(x,t)
y2 = @(t,y,z) y.^2 -0.1*exp(-t).*z

y1 and y2 are anonymous functions.

    y1=y0+(k1+k2)/2;
    y2=z0+(L1+L2)/2;

Not anymore they aren't! Now they are numeric variables !

[Jing Kai Wong]

Thank you!

Answer 2

[Ahmad]

Hi Wong

You destroyed y1 and y2 functions in for loop;

mabe be this works

clc
y1= @(t,y,z) -exp(-t).*y^2  %Write your f(x,t) function, where dy/dt=f(x,t)
y2 = @(t,y,z) y.^2 -0.1*exp(-t).*z
t0= 0; %initial value of t(0) 
y0= 1; %initial value of y(0)
z0 = 0;
h= 0.5; %step size
 %Formula: k1=h*f(x0,y0);  k2=h*f(x0+h,y0+k1); y1=y0+(k1+k2)/2;     
for i=1:2
    k1=h*y1(t0,y0,z0);
    L1 = h*y2(t0,y0,z0);
    t1=t0+h; 
    k2=h*y1(t1,y0+k1,z0+L1);
    L2 = h*y2(t1,y0+k1,z0+L1);
    y11=y0+(k1+k2)/2;
    y22=z0+(L1+L2)/2;
    t0=t1;
    y0=y11;
    z0=y22;
end
y11 %ans
y22
t1