how to fix limits are too large on heat equation

Hi, I am trying to run an explicit heat equation . This is the prompt I am trying to solve:

My code below

S0 = 10:10:100;
K = 50;
r = .05;
T = 2;
sigma = .2;
price = blsprice(S0,K,r,T,sigma)
amax = 10;
amin = -10;
M = [10 100 200 400 800];
N = [10 100 200 400 800];
for k = 1:5
      dx = (amax - amin)/(M(k)-1);
      dt = T/(N(k)-1);                         
      v = zeros(M(k), N(k));                       
      r= dt/dx^2;                          
      j = r/.5*sigma;
      x = linspace(amin,amax,M(k));
      v(:,1) = max(exp(.5*(j+1)*x) - exp(.5*(j-1)*x),0);               
         for n = 2:N(k)                      
           %2 lines below are initial and boundary conditions
             v(1,n) = v(1, 1);            
              v(N(k),n) = v(M(k),1);
             %line below is explicit method discretized
              v(2:M(k)-1,n) = (1-2*r)*v(2:M(k)-1,n-1)+r*v(1:M(k)-2,n-1)+r*v(3:M(k),n-1);
         end
         approx = v(2:M(k)-1,n)
  end
      error = abs(approx - price)  
     B= table(approx')
     G=table(price')
surf(v)

I get limits are too large error Any advice?

[Bob Thompson]

Could you post the entire error message, including which line of your code triggers it, please?

[Janvier Solaris]

This is the result when I run the code: G =

10×1 table

       Var1   
    __________

    4.9672e-08
     0.0047941
       0.33759
        2.6159
        8.0634
        15.982
        25.178
        34.896
        44.802
        54.772

error =

Columns 1 through 10

   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN
 NaN   NaN

Limits are too large

Limits are too large

I don't know if my boundaries are wrong or..... I am supposed to plot So vs error but I get NaN for my solution leading to the limits are too large. My code is to run this for different values of M and it works up to 200 but then it stops working

[Greg]

Doesn't help the question, but it's a fairly serious matter worth addressing. The line

error = abs(approx - price)

overrides a very crucial MATLAB function with a variable definition. Shadowing a function with a variable usually won't cause any major headaches, but error is potentially catastrophic.

I assume variable scope is keeping you safe, but it isn't a good thing to rely on.

[Janvier Solaris]

thank you Greg have corrected it continuing to work on it to fix the other problems

[Greg]

@Bob Nbob: I ran his code (a rare case of copy-paste actually works from a post, way to go Janvier!) and surprisingly, "Limits are too large" x2 is the entire error message.

@Janvier: Digging in, the error is coming from surf(v), and probably because much of v is NaN & Inf. I am guessing you are having a mix of initial/boundary conditions and indexing issues. Without knowledge of your field, I can't help identify where/what.

Answer 1

[Walter Roberson]

Your v values are generating +inf and -inf because of the exp() and the fact that j gets large.

Then surf() is complaining because you are trying to plot data with such a large range. Although it will skip the +inf and -inf data, you also have data in the +/- 1E308 range. Historically, plots could not be done if the difference between the min and max exceed the capacity of single()