Some technical issues of Laplace Numerical Equations

Hi there, I got some error message from the coding.

The codes are shown below.

When I run with it, it says I have the message as

Index in position 1 exceeds array bounds (must not exceed 1).

Error in section_2_b (line 42)

unkp1 = 0.25*(un(j+1,i)+un(j-1,i)+un(j,i+1)+un(j,i-1));

I am not sure how to figure it out : (

The method I am using is based on

clear;clc;close all;
T1 = -5;        % degree celcus
T2 = -10;       % degree celcus
L  = 3;         % metres [m] % length of the x dimensions
H  = 1;         % metres [m] % length of the y dimensions
nfs = 100;                                       % Number of Fourier terms
% Initialise error and set tolerance for convergence
err = 1;
tol = 1e-8;
k = 0;          % iteration counter
%% Method B
% Set the dx and dy
n = 1;
h = 0.1/(2^n);              % dx and dy has the same value
dx = h;
dy = h;
nx = L/h + 1;               % Number of grid points in x
ny = H/h + 1;               % Number of grid points in y
x  = linspace(0,L,nx);                           % Vector of grid points in x
y  = linspace(0,H,ny);                           % Vector of grid points in y
% Initialise the exact, numerical method
un = zeros(ny,nx);
unkp1 = zeros(ny,nx);
% Set boundary conditions
un(:,1) = 0;   % Left boundary
un(:,nx) = 0; % Right boundary
un(1,:) = -4*T2*x.*(x-L)/L/L;   % Bottom boundary
un(ny,:) = -4*T1*x.*(x-L)/L/L; % Top boundary
unkp1 = un;
% interate Jacobi Method(known as method B) till convergence
while err > tol
    % update itteration counter
    k = k + 1;
    % loop with computaional nodes
    for i = 2:nx - 1
        for j = 2:ny - 1
            unkp1 = 0.25*(un(j+1,i)+un(j-1,i)+un(j,i+1)+un(j,i-1));
        end
    end 
   % calculate the error
   err = sqrt(sum(sum((un-unkp1).^2)));
   % update un
   un = unkp1;
end
disp(un);

Answer 1

[KSSV]

Replace this line:

unkp1 = 0.25*(un(i+1,j)+un(i-1,j)+un(i,j+1)+un(i,j-1));

with

unkp1(i,j) = 0.25*(un(i+1,j)+un(i-1,j)+un(i,j+1)+un(i,j-1));

[Michael Wang]

Thanks a lot : )