Why are values in my loop filled with NaN?

Hello,

Can anyone tell why 'u' and 'v' inside my loop are all being filled with NaN? I cant figure out what I'm doing wrong. Thanks!

close all;
clear all;

a = 0;
b = 20;
nel = 200; % number of elements
h = (b-a)/nel; % step size
nv = nel+1;% number of vertices

x = a:h:b; % mesh
dt = 0.001; % time steps
tend = 20; 

e=ones(nv, 1);
%Discretization of the Laplace operator
Delta=1/(h^2)*spdiags([e -2*e e], -1:1, nv, nv);
Delta(1,2) = 2/h^2;
Delta(end,end-1) = -2/h^2;

% parameters of the model
eps = 0.02;
alpha = 0.1;

% initial guess
u = 0.5 * (x < 3);
v = 0 * x;

counter = 1;

% explicit Euler scheme
for t=dt:dt:tend
    
      u = u + dt/eps*(u .*(1-u).*(u-alpha) - v - ((Delta * u')'));
      v = v + dt * (u - v);
end

figcure(1)
plot(x,u,x,v,'r');
legend('u','v')
title('Solution of the Fitz-Hugh-Nagumo system')

Answer 1

[Stephen23]

Actually this has nothing to do with division by zero. When you read the NaN help it lists several ways that NaNs can occur:

"These operations produce NaN:"

• "Any arithmetic operation on a NaN, such as sqrt(NaN)"
• "Addition or subtraction, such as magnitude subtraction of infinities as (+Inf)+(-Inf)"
• "Multiplication, such as 0*Inf"
• "Division, such as 0/0 and Inf/Inf"
• "Remainder, such as rem(x,y) where y is zero or x is infinity"

In your case your code has increasingly large values in both u and v until on the eighth iteration they include several Inf elements (which critically have the same locations in both arrays):

>> any(any(isinf(u)==isinf(v))) % colocated Inf values.
ans = 1
>> any(isnan(u(:)))
ans = 0
>> any(isnan(v(:)))
ans = 0

Thus on the ninth iteration you calculate this: v - ((Delta * u')'), which is thus a subtraction of infinities and (exactly as the documentation states) produces NaNs:

>> tmp = v - (Delta * u')';
>> any(isnan(tmp(:)))
ans = 1