Can anybody help me understanding this mentioned line of code?

Nx=100;
FldLngt=8e-3; 
DeltLngt=FldLngt/Nx;
--->PDz2(i,j)=(P(i-1,j-1)+P(i,j-1)+P(i+1,j-1)+P(i-1,j)+P(i+1,j)+P(i-1,j+1)+P(i,j+1)+P(i+1,j+1)-8*P(i,j))/(DeltLngt^2*2);<---
PDt2(i,j)=C(i,j)^2*PDz2(i,j);

where

Nx=grid points in x direction
FldLngt= length of simulation field
Delt is for Delta
PDz2= 2nd derivation of pressure with respect to z direction
PDt2=2nd derivation of pressure with respect to time t

I know that it is wave equation calculated using laplacian mask but i couldn't understand the denominator in mentioned line.

Answer 1

[Roger Stafford]

The numerator is the Laplacian under the assumption that there is unit distance spacing between adjacent grid points of the pressure array P. The ‘DeltLngt^2’ in the denominator corrects this so that it becomes the Laplacian assuming the actual distance values between adjacent grid points in both the x and y directions. I don’t know what the ‘2’ means in the denominator.

[lurkingleo]

thanks for helping me out..This '2' was confusing me also. Can you please explain these lines too i couldnt find which equation of pressure is applied here.

PDt1(i,j)=PDt2(i,j)*DeltT+PDt1(i,j); P(i,j)=PDt1(i,j)*DeltT+P(i,j);

where DeltT=0.04e-6; %time step;