| Class | Description |
|---|---|
| ExplicitCentralDifference1D |
This explicit central difference method is a numerical technique for solving
the one-dimensional wave equation by the following explicit
three-point central difference equation.
\[
\frac{u^{k+1}_j - 2u^k_j + u^{k-1}_j}{\Delta t^2}
= \beta \frac{u^{k}_{j+1} - 2u^k_j + u^{k}_{j-1}}{\Delta x^2}
\]
where \(u^k_j = u(t_k, x_j)\) is the estimate at \((k, j)\) in the grid.
|
| WaveEquation1D |
A one-dimensional wave equation is a hyperbolic PDE that takes the following form.
\[
\frac{\partial^2 u}{\partial t^2} = \beta \frac{\partial^2 u}{\partial x^2}
\]
with both boundary ends fixed at 0, that is,
\[
u(t, 0) = u(t, a) = 0
\]
and two initial conditions, namely u and its first time derivative \(u_{t}\):
\[
u(0, x) = f(x), 0 < x < a \\
u_t(0, x) = g(x), 0 < x < a
\]
|
Copyright © 2010-2026 NM Group. All Rights Reserved.