Abstract: We applied variational iteration method to solve periodic boundary value problems. A correction function can be easily constructed by Lagrange multiplier which can be identified by variation theory. The initial approximation can be selected with unknown parameters which can be determined via boundary value conditions. Comparing the approximate with the exact solution of two concrete examples, we can find that the variation iteration method is convenient and efficient.

Key words: variational iteration method, periodic boundary value problems, variation theory, Lagrange multiplier