Approximate Ad Hoc Parametric Solutions for Nonlinear First-Order PDEs Governing Two-Dimensional Steady Vector Fields

Figure 2

(a) 𝑢₁(×10²) versus 𝑥₁, 𝑀=0.7, sinusoidal shape: 𝑎_𝑠=0.05, 𝑏=0.5; (b) 𝑢₁(×10²) versus 𝑥₁, 𝑀=0.7, sinusoidal shape: 𝑎_𝑠=0.05, 𝑏=0.5, Ad hoc parametric solution (black line)—linearized equation (blue line); (c) 𝑢₂ versus 𝑥₁, 𝑀=0.7, sinusoidal shape: 𝑎_𝑠=0.05, 𝑏=0.5.

(a)

(b)

(c)