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solve ODE using finite difference method

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Emon Baroi
Emon Baroi 2023-2-8
回答： SAI SRUJAN 2024-8-13，9:49
du/dt=d^2u/dx^2

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回答（2 个）

Torsten
Torsten 2023-2-8
This is a PDE, not an ODE.
Use "pdepe" to solve.
SAI SRUJAN
SAI SRUJAN 2024-8-13，9:49
Ran in:
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!

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