Furthermore, suppose that v(t) is the unique solution to the I.V.P.
Then the linear combination
is a solution to with .
Program (Linear Shooting Method):
To approximate the solution of the boundary value problem
over the interval [a,b] by using the Runge-Kutta method of order n=4.
The method involves solving a two systems of equations over . First solve
Finally, the desired solution x(t) is the linear combination
The subroutine Runge2D will be used to construct the two solutions , and .