I am getting Index exceeds the number of array elements(1) error?

I have attached my code

close all
clear all
clc

% Input values
n = 31;
x = linspace(0,3,n);
dx = x(2)-x(1);
gamma = 1.4;

% Calculate initial profile
rho = 1-0.3146*x; % Density
t   = 1-0.2314*x; % Temperature
v   = (0.1+1.09*x).*t.^0.5; % Velocity
a   = 1+2.2*(x-1.5).^2; %Area

% Time steps
nt = 100;
dt = 0.001;
% Outer time loop
for k=1:nt
    rho_old = rho;
    v_old = v;
    t_old = t;
    
    % Predictor step
    
    % Continuity Equation
    for j = 2:n-1
    %drho_dt_p = -rhodv_dx-rhovdloga_dx-vdrho_dx main equation
    % Sepearting the terms for easy debugging 
    dv_dx    =  (v(j+1)-v(j))/dx;
    dloga_dx =  (log(a(j+1))-log(a(j)))/dx;
    drho_dx  =  (rho(j+1)-rho(j))/dx;
    dt_dx    =  (t(j+1)-t(j))/dx;
        
    drho_dt_p = -rho(j)*(dv_dx-rho(j))*v(j)*(dloga_dx-v(j))*(drho_dx);
    
    % Momentum Equation
    dv_dt_p = -v(j)*dv_dx-(1/gamma)*((dt_dx)+(t(j)/rho(j))*drho_dx);
    
    % Energy Equation
    dt_dt_p = -v(j)*dt_dx-(gamma-1)*t(j)*((drho_dx)+v(j)*dloga_dx);
   % Solution Update
    rho(j) = rho(j)+drho_dt_p(j)*dt;
    v(j)   = v(j)+dv_dt_p(j)*dt;
    t(j)   = t(j)+dt_dt_p(j)*dt;
    
    end 
end

[Jan]

You do get an error message, which tells, in which line the error occurs. It helps to solve your problem, if you share this important information with the readers.

Answer 1

[Jan]

With guessing where the error occurs:

    dv_dt_p = -v(j)*dv_dx-(1/gamma)*((dt_dx)+(t(j)/rho(j))*drho_dx);
    dt_dt_p = -v(j)*dt_dx-(gamma-1)*t(j)*((drho_dx)+v(j)*dloga_dx);    

Both variables are scalars. Then indexing them with j does not work:

    rho(j) = rho(j)+drho_dt_p(j)*dt;
    %                        ^^^ omit this
    v(j)   = v(j)+dv_dt_p(j)*dt;
    %                    ^^^ omit this
    t(j)   = t(j)+dt_dt_p(j)*dt;
    %                    ^^^ omit this    

Use the debugger to find the cause of such problems:

    dbstop if error    

Then run the code until Matlab stops. Now check, which of the indices is out of range:

j
size(v)
size(dv_dt_p)
size(drho_dt_p)

[KALYAN ACHARJYA]

Yes sir, I noticed that ..thanks for clarification.