D0 Boundary Conditions in the Falkner-Skan Adjoint Expansion

Numerical verification that D0(0)=1 and D0(∞)=0 for the adjoint eigenfunction series across pressure-gradient parameter β∈[0,2]

9
β Values Tested
10-12
Best D0(0) Residual
1.0
w1·D1(0) for All β

D0 Boundary Verification (BVP vs Shooting)

Far-Field Residual |D0(ηmax)|

First-Mode Dominance: D1(0) = 1/(1+β)

Series Convergence SN(0) → 1

Detailed Results Table

βBVP D0(0)BVP D0(∞)Shoot D0(0)Shoot D0(∞)D0'(0)D0''(0)

Base Flow: Falkner-Skan Wall Shear F''(0)

βF''(0)