solve ODE using finite difference method

du/dt=d^2u/dx^2

Answer 1

[Torsten]

This is a PDE, not an ODE.

Use "pdepe" to solve.

Answer 2

[SAI SRUJAN]

Hi Emon,

I understand that you are trying to solve a pde using finite difference method.

Refer to the following code sample to proceed further,

Nx = 50;        % Number of spatial points
Nt = 1000;      % Number of time steps

% Discretization
dx = 1 / (Nx - 1);
dt = 0.1 / Nt;
x = linspace(0, 1, Nx);
t = linspace(0, 0.1, Nt);

% Stability condition
if dt > dx^2 / (2)
    error('Time step is too large for stability.');
end

% Initial condition
u = sin(pi * x); 

% Time-stepping loop
for n = 1:Nt
    u_new = u; 
    for i = 2:Nx-1
        % Finite difference approximation
        u_new(i) = u(i) +dt / dx^2 * (u(i+1) - 2*u(i) - u(i-1));
    end
    u = u_new; 
end

plot(x, u);
xlabel('x');
ylabel('u');
title('Solution of the PDE \partial u/\partial t = \partial^2 u/\partial x^2');

I hope this helps!