I get the warning 'Function behaves unexpectedly on array inputs.' when using fplot()

Why do I get a warning when using fplot() in my code:

function solution_heat_equation(t)
f = @(x,y) (exp((-abs(x-y).^2)./(4.*t))).*u_0(y);
a = -10;
b = 10;
z = @(x) integral(@(y) f(x,y) , a,b);
u = @(x) (1/sqrt(4*pi*t))*z(x)

fplot(u)

function val = u_0(x)
if abs(x)<1 
    val = 1;
else
    val = 0;
end

I get the following warning and I don't get a plot of my function:

Warning: Function behaves unexpectedly on array inputs. To improve performance, properly
vectorize your function to return an output with the same size and shape as the input
arguments. 
> In matlab.graphics.function.FunctionLine>getFunction
  In matlab.graphics.function/FunctionLine/updateFunction
  In matlab.graphics.function.FunctionLine.set.Function_I
  In matlab.graphics.function.FunctionLine.set.Function
  In matlab.graphics.function.FunctionLine
  In fplot>singleFplot (line 245)
  In fplot>@(f)singleFplot(cax,{f},limits,extraOpts,args) (line 200)
  In fplot>vectorizeFplot (line 200)
  In fplot (line 166)
  In solution_heat_equation (line 8) 

Answer 1

[Star Strider]

With a scalar ‘t’, there are no problems provided that ‘z’ sets 'ArrayValued' to true in the integral call, and ‘u’ is vectorised:

z = @(x) integral(@(y) f(x,y) , a,b, 'ArrayValued',1);
u = @(x) (1./sqrt(4*pi*t)).*z(x);

The rest of your code is unchanged.

[LM]

I still get the warning but the plot is working. Thanks a lot!

[Star Strider]

As always, my pleasure!