Finite-Difference Method for PDEs
PDE
Heat equation:
$\partial_t u = \partial_x^2 u$
Transport:
$\partial_t u + c\partial_x u=0$
Drift-diffusion:
$\partial_t u + c\partial_x u= \partial_x^2 u$
Eikonal:
$u_t = |u_x|$
Hamilton-Jacobi:
$u_t + |u_x|^2 = 0$
Burgers:
$u_t + u u_x = 0$
Boundary conditions
Periodic:
$u(0,t)=u(\ell,t)$
Dirichlet:
$u(0,t)=u(\ell,t)=0$
Neumann:
$u_x(0,t)=u_x(\ell,t)=0$
Initial condition $u_0$
Draw
$u_0(x)$ =
Parameters
Set
Time =
N =
dt =
Iteration scheme
u[i]=
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