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

I have a piece of code, but I don't know how to fix the error

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

Error in Homework_8_GFDM (line 33)

h_t(j,i) = h_t(j,i-1) - (t_step/x(j)) * (Q_t(j,i-1)/A(j,i-1) - Q_t(j-1, i-1)/A(j-1,i-1));

clear; close all;

% Input parameters
b = 6.1;        % Channel bottom width (m)
z = 1.5;        % Side slope (H:V)
Q = 126;        % Flow rate (m^3/s)
h = 5.79;       % Flow depth (m)
S0 = 0.00008;   % Channel bed slope
n = 0.013;      % Manning's roughness coefficient
L = 5000;       % Channel length (m)
t_end = 2000;   % Calculation time (s)
t_step = 1;     % Time step (s)

% Initial parameter calculations
A = b*h + z*h^2;     % Cross-sectional area (m^2)
P = b + 2*h*sqrt(1+z^2); % Wetted perimeter (m)
R = A/P;            % Hydraulic radius (m)
V = Q/A;            % Flow velocity (m/s)
Fr = V/sqrt(9.81*h); % Froude number
Sf = n^2 * V^2 / R^(4/3); % Energy slope

% Transient condition calculations
x = linspace(0, L, 101);
t = 0:t_step:t_end;
h_t = zeros(length(x), length(t));
Q_t = zeros(length(x), length(t));
h_t(:,1) = h;
Q_t(:,1) = Q;

for i = 2:length(t)
    for j = 2:length(x)-1
        if j > 1
            h_t(j,i) = h_t(j,i-1) - (t_step/x(j)) * (Q_t(j,i-1)/A(j,i-1) - Q_t(j-1,i-1)/A(j-1,i-1));
        else
            h_t(j,i) = h_t(j,i-1) - (t_step/x(j)) * (Q_t(j,i-1)/A(j,i-1) - 0/A(j,i-1));
        end
        if j < length(x)-1
            Q_t(j,i) = Q_t(j,i-1) - (t_step/x(j)) * (9.81*A(j,i-1)*(h_t(j+1,i-1) - h_t(j-1,i-1))/(2*x(j)) + 9.81*A(j,i-1)*S0 - Sf(j,i-1)*Q_t(j,i-1)^2/A(j,i-1)^2);
        else
            Q_t(j,i) = 0; % Flow rate is zero at the end point
        end
    end
    h_t(1,i) = h_t(2,i); % Boundary condition at upstream
    Q_t(1,i) = Q_t(2,i);
    h_t(end,i) = h_t(end-1,i) - (t_step/x(end)) * (Q_t(end,i-1)/A(end,i-1) - Q_t(end-1,i-1)/A(end-1,i-1)); % Boundary condition at downstream
    Q_t(end,i) = 0; % Flow rate is zero at the end point
end

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

% Plotting graphs
figure;
plot(x/1000, h_t(:,1), 'b-', x/1000, h_t(:,51), 'r-', x/1000, h_t(:,101), 'g-', x/1000, h_t(:,151), 'c-', x/1000, h_t(:,201), 'm-');
legend('t = 0 s', 't = 500 s', 't = 1000 s', 't = 1500 s', 't = 2000 s');
xlabel('Distance (km)'); ylabel('Flow depth (m)');
title('Flow depth variation along the channel');

figure;
plot(t, h_t(15,1:end), 'b-', t, h_t(25,1:end), 'r-', t, h_t(30,1:end), 'g-', t, h_t(50,1:end), 'c-');
legend('x = 1.5 km', 'x = 2.5 km', 'x = 3 km', 'x = 5 km');
xlabel('Time (s)'); ylabel('Flow depth (m)');
title('Flow depth variation over time');

Answer 1

[Torsten]

A is a single value, namely

A = b*h + z*h^2;     % Cross-sectional area (m^2)

But in your double loop, you treat A as if it were a matrix of size [length(x),length(t)].

[Thai An]

yes, thank you so much, because i just start simulate with matlab in two days ago