| Abstract: | A new variational principle is proposed for determining the asymptotic expansion of the solution of the Ackerberg-O'Malley resonance problem Stud. Appl. Math. 49:277–295 (1970)] to any order in ε. The method used yields new higher-order results not permitted by the technique of Grasman and Matkowsky SIAM J. Appl. Math. 32:588–597 (1977)]. Explicit results using the method are reported to O(ε) and confirmed with asymptotic expansions of the exact solution; the O(1) results agree with those reported in the literature. In the case where the coefficient functions are analytic, an exact solution is presented. It is not difficult to perform the higher-order calculations using the proposed variational approach, in contrast to the current methods in use. |
