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.