how to developed numerical code for collocation method for linear differential equations

please sr/ ma'am

our big problem to creat code in MATLAB

i can't undestand , how to write down the diifential equation and boundary condition in matlab

[Alan Stevens]

What is the equation and what are the boundary conditions?

[Anup Negi]

[Anup Negi]

Can you send your eamil I'd sr

Answer 1

[Alan Stevens]

I've just noticed you want to use a collocation method. So you proceed as follows

% For method of collocation choose a functional form for U
% Suppose, for simplicity you choose a simple parabola
% u(z) = a + b*z + c*z^2     (u is potential approximate version of U)
% dudz(z) = b + 2c*z 
% d2ud2 = 2*c
% where a, b and c are constants to be determined.
% 
% The actual ODE is
% d2Udz2 + A*dUdz + B = 0  where (presumably) you know A and B.
% 
% so with your approximate solution this would become
% 2c + A*(b + 2c*z)+ B = 0 
% choose a collocation point, z = zcol, say and this becomes
% 2c + A*(b + 2c*zcol)+ B = 0  ...(1)
% 
% Assuming you know U on your boundaries, z = eta and z = 1 you also have 
% U(eta) = a + b*eta + c*eta^2  ...(2)
% U(1) = a + b + c              ...(3)
% 
% You now have three equations with which to find a, b and c
% This can be done easily with
%  M = [0  A  2+2*A*zcol; 1  eta  eta^2; 1  1  1];
%  V = [-B; U(eta); U(1)];
%  [a; b; c] = M\V;
%
% so your approximate solution is: u(z) = a + b*z + c*z^2
% 
% If you want to use more collocattion points you'll need to 
% choose a higher order approximate equation.