Two-Point Boundary Value Problems
|Solve y″ = f(x, y, y′), y(a) = α, y(b) = β.|
In two-point boundary value problems the auxiliary conditions associated with the differential equation, called the boundary conditions, are specified at two different values of x. This seemingly small departure from initial value problems has a major repercussion—it makes boundary value problems considerably more difficult to solve. In an initial value problem we were able to start at the point where the initial values were given and march the solution forward as far as needed. This technique does not work for boundary value problems, because there are not enough starting conditions available at either endpoint to produce a unique solution. ...