Elliptic PDE-Laplace Equation. Heated in the center of the square plate

#Laplace #elliptic #PDE #Matlab #finitedifferences
Elliptic PDE-Laplace Equation. Heated in the center of the square plate.
clc;clear;close all;
x0=0; xf=1;
y0=0; yf=1;
nx=121; ny=121;
x=linspace(x0,xf,nx);
y=linspace(y0,yf,ny);
dx=x(2)-x(1);
dy=y(2)-y(1);
T=zeros(nx,ny); %preallocation matrix
% Calculate the center coordinates of the matrix
%www.mathworks....
[rows, cols] = size(T);
center_row = ceil(rows/2);
center_col = ceil(cols/2);
% Define the size of the mini square
square_size = 4;
% Calculate the starting row and column indices of the mini square
start_row = center_row - floor(square_size/2);
start_col = center_col - floor(square_size/2);
% Extract the mini square
T_center = T(start_row:start_row+square_size-1, start_col:start_col+square_size-1);