ABSTRACT
Boundary-value problems (BVP) can be solved numerically by using either the shooting method or the finite-difference method. To apply the shooting method, the BVP is first made into an initial-value problem (IVP) by guessing at the initial condition(s) that are obviously absent in the description of a BVP. The shooting method relies on techniques such the fourth-order Runge-Kutta method (RK4) for solving IVP. The shooting method loses its efficiency when applied to higher-order BVP, which will require more than one guess for the initial values. BVP can be based on differential equations with orders higher than two, which require additional boundary conditions. The most common boundary conditions are Dirichlet boundary conditions, Neumann boundary conditions and mixed boundary conditions. In the case of mixed boundary conditions, information involving the derivative of the dependent variable is prescribed at one or both of the endpoints of the domain of solution.
