Matrix dimensions must agree.

Hello,

I had a problem with this:

clear;clc
t0=0;
tf=5;
Emax=1e-9;
Emin=1e-10;
hmax=2e-1;
hmin=1e-3;
nmax=1e4;
f=@(u,t) -u+exp(-t);
x0=0;
wyn=zeros(1,nmax);
time=zeros(1,nmax);
t=t0;
wyn(1)=x0;
h=1e-2;
Es=zeros(1,nmax);
time(1)=t0;
i=1;
k=zeros(6,1);
W4=[25/216,1408/2565,2197/4104,1/5];
W5=[16/135,6656/12025,28561/56430,9/50,2/55];
while(t<tf && i<nmax)
    if h<hmin
        h=hmin;
    end
    if h>hmax
        h=hmax;
    end
    k(1)=h*f(t,wyn(i));
    k(2)=h*f(t+1/4*h,wyn(i)+1/4*k(1));
    k(3)=h*f(t+3/8*h,wyn(i)+3/32*k(1)+9/32*k(2));
    k(4)=h*f(t+12/13*h,wyn(i)+1932/2197*k(1)-7200/2197*k(2)+7296/2197*k(3));
    k(5)=h*f(t+h,wyn(i)+439/216*k(1)-8*k(2)+3680/513*k(3)-845/4104*k(4));
    k(6)=h*f(t+1/2*h,wyn(i)-8/27*k(1)+2*k(2)-3544/4104*k(3)+1856/4104*k(4)-11/40*k(5));
    R4=wyn(i)+sum(W4.*k(1:end-1));
    R5=wyn(i)+W5.*k;
    Ek=abs(R5-R4);     - here is a problem.
    if Ek>Emax
        h=1/2*h;
    else 
    x(i+1)=R5;
    time(i+1)=t;
    if Ek<Emin
        h=2*h;
    end
    t=t+h;
    i=i+1;
    end
end
wyn=x(1:i-1);
time=time(1:i-1);

In line 37 is some problem can someone help me what i did wrong here?

Thanks For help.

Answer 1

[Adam Danz]

At line 37 (the line that contains Ek=abs(R5-R4)), the variable R5 is a [6x5] matrix while R4 is [1x4]. When subtracting matrices, the dimensions must agree (as the error message indicates).

It would take quite a bit of effort to reverse engineer your code to figure out what it's supposed to be doing and then suggest a correction. I can more quickly identify potential sources of the problem.

The 2 lines below produce two different sized vectors.

W4=[25/216,1408/2565,2197/4104,1/5];                % [1 x 4]
W5=[16/135,6656/12025,28561/56430,9/50,2/55];       % [1 x 5]

Since 'k' is a [6 x 1] vector, when you multiply k by W5, you produce a [6 x 5] matrix.

The [1 x 4] vector stored in R4 is a result of this line: sum(W4.*k(1:end-1)). Here, W4 is [1 x 4] while k is [6 x 1] and the result of the multiplication is [5 x 4] but then you're taking the sum over the 2nd dimension making it [1 x 4].

Long story short, there's probaby a vector with the wrong orientation (column vs row) or perhaps the W4 and W5 vectors should have the same length. You'll need to sift through the code, line by line, to make sense of it.

Answer 2

[Pawel Kostyra]

Well at the end I have to determine the characteristics representing the real error, estimated error. But, if i have error in code I cant use plot function.

Even if i use your code:

    R4=wyn(i)+sum(sum(W4.*k(1:end-1)));    

Like u said this function still working and i can't get a last view.

I did somethink wrong. Well i will try repair it.

Thanks For Help.

[Adam Danz]

Fortunately your code isn't very long. I suggest going through your code line by line starting at the top. Compare the results of each line with the expected results.

If you're getting a matrix where you expect to get a single value, you might need to transpose a vector or put a dot in front of multiplication or division symbols.