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 $u_0$

$u_0(x)$ =

Parameters

Time =
N =
dt =

Iteration scheme

u[i]=

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