Hyperbolic PDE — Wave Equation & Characteristics
u_tt = c²u_xx — d'Alembert solution, Riemann invariants, characteristic curves
Parameters
Wave speed c:
1.5
Damping γ:
0.01
Initial condition:
Gaussian pulse
Sine wave
Triangle pulse
Step function
Boundary condition:
Fixed ends
Periodic
Open (absorbing)
Reset
Pause
u_tt = c²u_xx − γu_t
d'Alembert: u(x,t) = f(x−ct)+g(x+ct)
Characteristics: x±ct = const
CFL condition: c·Δt/Δx ≤ 1
Riemann invariants: R± = u_t ± cu_x
Time t:
0.00
Energy:
—
CFL:
—