Generalized Perturbation Method for Solving Two-Point Boundary-Value Problems

A method for solving two-point boundary-value problems is presented, and since it contains the standard perturbation method as a subcase, it is referred to as the generalized perturbation method. The philosophy of the method is to iterate on the histories of the variables whose initial values are unknown. For problems of a physical origin, it is not difficult to make reasonable guesses for these functions. Because variable histories are being used and not just the initial values, the generalized perturbation method is much less sensitive to the guesses than the standard perturbation method. More storage and computation per iteration is required, but the number of iterations may be considerably less.