Numerical Solution of Boundary-Value Problems
In Chapter 7, we learned that an initial-value problem refers to the situation when an nth-order differential equation is accompanied by n initial conditions, specified at the same value of the independent variable. It was also mentioned that in other applications, these auxiliary conditions may be specified at different values of the independent variable, usually at the extremities of the system, and the problem is known as a boundary-value problem (BVP).
Boundary-value problems can be solved numerically by using either the shooting method or the finite-difference method. To apply the shooting method, the boundary-value problem is first made into an initial-value problem (IVP) by guessing ...
