Here the functions f'i are known. If it is a two-point boundary value problem, then there are two classes of numerical methods to solve the problem. In general the solution values of y i at the final point will deviate from the required known n 2 boundary values there. Now we adjust the free initial point parameters to reduce the deviations at the final point. Iterations of this procedure are continued until the desired accuracy is achieved.
Relaxation methods use a different approach.
These methods are preferred over shooting method when the solutions are smooth and not highly oscillatory. As is the case for the example introduced above, the boundary value problem may contain a parameter, denoted there by l . Then solutions may not be possible for arbitrary values of l . A slight modification of the procedure is then made using the following trick. The solution is again found by interation starting with a guess for free initial conditions.