Find five correct decimals of temp at x

If I have a plot, how can I find the temperature at x=1 with five accurate decimals? It must be a way in which I have compared and can trust that the decimals are in fact accurate.

For example, say this is my code:

clear all, close all, clc

L=3.4;
N=100;
T0=300;
Tslut=410;
h=L/N;
x=linspace(0,L,N+1);
x=x.';
fk=@(x)2+x/7;
fQ=@(x)260*exp(-(x-L/2)^2); 
A=zeros(N+1);
b=zeros(N+1,1);
A(1,1) = 1.0;
b(1) = T0;
for i=2:N
  xp=x(i);
  xhl=xp-h/2;
  xhr=xp+h/2;
  A(i,i-1) = -fk(xhl); 
  A(i,i)   = (fk(xhl)+fk(xhr));
  A(i,i+1) = -fk(xhr);
  b(i) = fQ(xp)*h^2;
end
A(N+1,N+1) = 1.0;
b(N+1) = Tslut;
T=A\b;
plot(x,T)

All help is appreciated!

Answer 1

[Alan Stevens]

How about using

T1 = interp1(x,T,1);

Use a finer mesh of x values if the result isn't satisfactory.

[Katara So]

I thought about using that however our professor said that we have to show what makes us trust the five decimals. I don't really know how interp1 works and therefore I don't know if the answer given is trustworthy. Would be a good enough way of checking the decimals?