Abstract: The exact analytic method was given by [1].It can be used for arbitrary variable coefficient differential equations and the solution obtained can have the second order convergent precision.In this paper, a new high precision algorithm is given based on [1], through a bending problem of variable cross-section beams.It can have the fourth convergent precision without increasing computation work.The present computation method is not only simple but also fast.The numerical examples are given at the end of this paper which indicate that the high convergent precision can be obtained using only a few elements.The correctness of the theory in this paper is confirmed.

Key words: exact analytic method, bending of beam, high convergent precision