General

General

1. Linear Operators

   • L(u+v) = L(u) + L(v)
   • L(cu) = cL(u)
   • Only satisfied by linear Equations

2. Linearisation of Equations

   • 1. Look for Background/Equilibrium Solutions
     • Φₒ determined by finding: ODE(Φₒ) = 0
   • 2. Look for solutions that are small disturbances, Φ₁, about Φₒ
     • Φ = Φₒ + Φ₁
     • Substitute into ODE, letting all Φₒ solutions = 0
     • f(Φ₁)≈Φ₁ as very small