collect like terms, and substitute values for i

I have this equation:

dT = (a/r)*((T_i+1 - T_i-1)/2*dr) + r*((T_i+1 - T_i + T_i-1)/dr^2) + q/cp*rho;

I want to simplify this and collect like terms, as in T_i+1, T_i and T_i-1.

I also want to be able to plug in values for i, such as 1, n-2, n-1 and so on.

I tried a few things like this:

% Clear the workspace and the command window
clear; clc;

% Declare the symbolic variables
syms a dr T1 Ti T2 r q cp rho

% Define the expression
dT = (a/r)*((T1 - T2)/2*dr) + r*((T1 - Ti + T2)/dr^2) + q/cp*rho;

% Expand the expression to combine like terms
dT_expanded = expand(dT);

% Collect the terms for T1, Ti, and T2
[T1_coeff, T1_term] = coeffs(dT_expanded, T1, 'All');
[Ti_coeff, Ti_term] = coeffs(dT_expanded, Ti, 'All');
[T2_coeff, T2_term] = coeffs(dT_expanded, T2, 'All');

% Display the collected terms for T1, Ti, and T2
disp("Terms for T1:")

Terms for T1:

disp(T1_term)

disp("Terms for Ti:")

Terms for Ti:

disp(Ti_term)

disp("Terms for T2:")

Terms for T2:

disp(T2_term)

;;;;;;
%and more simply 
dT = simplify((a/r)*((T1 - T2)/2*dr) + r*((T1 - Ti + T2)/dr^2) + q/cp*rho)

dT = 

% Display the simplified expression
disp(dT);

a1 = collect(dT, T1)

a1 = 

b1= collect(dT, Ti)

b1 = 

c1=collect(dT, T2)

c1 = 

d1=q/(cp*rho)

d1 = 

But neither of these are giving me what I want.

Answer 1

[Walter Roberson]

You do not say clearly what you do want.

% Clear the workspace and the command window
clear; clc;

% Declare the symbolic variables
syms a dr T1 Ti T2 r q cp rho

% Define the expression
dT = (a/r)*((T1 - T2)/2*dr) + r*((T1 - Ti + T2)/dr^2) + q/cp*rho;

% Expand the expression to combine like terms
dT_expanded = expand(dT);

% Collect the terms for T1, Ti, and T2
[T1_coeff, T1_term] = coeffs(dT_expanded, T1, 'All');
[Ti_coeff, Ti_term] = coeffs(dT_expanded, Ti, 'All');
[T2_coeff, T2_term] = coeffs(dT_expanded, T2, 'All');

% Display the collected terms for T1, Ti, and T2
disp("Terms for T1:")

Terms for T1:

disp((T1_term == T1_coeff).')

disp("Terms for Ti:")

Terms for Ti:

disp((Ti_term == Ti_coeff).')

disp("Terms for T2:")

Terms for T2:

disp((T2_term == T2_coeff).')