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Transport Equation Explorer
u_t + c·u_x = 0
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Wave Parameter
Wave speed c
1.0
Initial Condition
Shape
Gaussian
Square Pulse
Sine Burst
Triangle
Double Gaussian
Asymmetric Pulse
Width σ
0.30
Amplitude A
1.0
Numerical Setup
Grid points N
200
CFL number ν
0.90
Scheme
Upwind (1st order)
Lax-Wendroff (2nd order)
Lax-Friedrichs
Centered (unstable!)
Display
Exact solution
Numerical solution
Initial profile
Grid dots
Fill under curve
Animation
Speed
0.1
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Loop at T
6.0
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Exact
Numerical
Initial
t = 0.000
ν = 0.90
u(x, t) — Solution Profile
|u_exact − u_numerical|
x–t Spacetime · Click to highlight a characteristic
All Schemes vs Exact
Transport · u_t + cu_x = 0 (numerical + exact dashed)
Diffusion · u_t = ν u_xx
Burgers · u_t + uu_x = 0
t = 0.000
dx = —
dt = —
L² = —
Scheme: Upwind
CFL ν = —
📖 Transport Equation — Theory Guide
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