fem1d_heat_implicit, a MATLAB code which solves the time-dependent 1D heat equation, using the finite element method in space, and an implicit version of the method of lines, using the backward Euler method, to handle integration in time.
This program solves
dUdT - k * d2UdX2 = F(X,T)over the interval [A,B] with boundary conditions
U(A,T) = UA(T), U(B,T) = UB(T),over the time interval [T0,T1] with initial conditions
U(X,T0) = U0(X)
The spatial derivatives are approximated using the finite difference method, with piecewise linear elements.
The solver applies an implicit backward Euler approximation to the first derivative in time.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
fem1d_heat_implicit is available in a MATLAB version.
fd1d_heat_implicit, a MATLAB code which uses the finite difference method and implicit time stepping to solve the time dependent heat equation in 1d.
fem1d_heat_explicit, a MATLAB code which uses the finite element method and explicit time stepping with the forward euler method to solve the time dependent heat equation in 1d.
fem1d_heat_steady, a MATLAB code which uses the finite element method to solve the steady (time independent) heat equation in 1d.