Knowledge card
Reduction to a First-order System
Mathematical Modelling — Fluid Dynamics & Heat TransferNumerical analysis; boundary-layer similarity theory
Symbol
The standard preprocessing every ODE integrator expects: introduce the state vector y = (f, f′, f″, θ, θ′), so the coupled system becomes five first-order equations y′ = F(η, y) — three trivial shifts plus the two solved curvatures.
Dimension I
Definition
What it is — and what it is not
- What it is
- S1The state vector y = (y₁,…,y₅) = (f, f′, f″, θ, θ′) turns the coupled system into five first-order equations: y₁′ = y₂, y₂′ = y₃, y₃′ = f‴(y), y₄′ = y₅, y₅′ = θ″(y).
Dimension II
In practice
How to deal with it
- How to deal with it
- S2Write the MATLAB ODE function to return exactly these five components; both bvp4c/bvp5c and the RK4 shooting integrator consume the same F(η, y).
copyright© owned by Webiscopic Sdn. Bhd. 2026. All right reserved.
vproductionmain @ 5d8445a3