midpoint, a FreeFem++ code which uses the (implicit) midpoint method to approximate the solution of a time dependent boundary value problem (BVP).

Our problem is posed on the unit square, with zero boundary conditions, and having the exact solution

        u = sin(pi x) sin(pi y) e^(-t)
The boundary value problem is posed as
        du    d^2 u   d^2 u
        -- -  ----- - ----- = (2 pi^2 - 1 ) sin(pi x) sin(pi y) e^(-t)
        dt    dx^2    dy^2
with initial condition at t=0:
        u(x,y,0) = sin(pi x) sin(pi y)
and boundary condition
        u(x,y,t) = 0


The computer code and data files described and made available on this web page are distributed under the MIT license


Source Code:

Last revised on 26 February 2021.