I am working on Modified Homotopy perturbation transformation method to solve a PDE. Referred paper is given below.
DOI 10.1007/s10598-015-9278-x
In the above paper, they got $w(r,t)$ as \begin{equation} w(r,t)=f(r)*\delta(t) \end{equation}
Where $\delta(t)$ is the Dirac's delta function and $f(r)$ is some function of $r$, the exact definition of $f(r)$ can be seen in the paper. Since that is not important here, I am not mentioning it here.
Then they have given the values of $w(r,t)$ for different values of $r$ when $t=0.2$ and $t=2$.
For example when $r=1.2$ and $t=0.2$, $w(r,t)=0.834044$ and when $r=1.2$ but when $t=2$, $w(r,t)=0.855111$.
My question is how to calculate $\delta(0.2)$ and $\delta(2)$? From the above equation that I mentioned here, we can see that the values of $w(1.2,t)$ are changing for different values of $t$ only depends on $\delta(t)$. How can we find the values of Dirac delta function exactly at some point?