Boundary Value Problems, Shooting Methods

• Convert the following third order ODE for boundary layers into a system of three coupled first order ODEs: $$2g^{\prime\prime\prime} + gg^{\prime\prime} = 0.$$
• What are two ways that boundary value problems (BVPs) differ from initial value problems (IVPs)?
• Is the following BVP linear or nonlinear? $$k\frac{d^2T}{dx^2} + \frac{dk}{dx}\frac{dT}{dx} = q$$
  • what if k = k(x)?
  • what if k = k(T)?
• What are the names (with correct spelling) of the three main types of boundary conditions?
  • what do these correspond to for the case of heat transfer?
• What are the two numerical methods presented for solving BVPs?
• How is the shooting method related to a nonlinear algebraic problem?
• Describe shooting method in your own words. What is the idea, what are the steps?
• Besides the gas stripper example given, give another physical system governed by a BVP that could be solved using a shooting method.