The asymptotic numerical solution of highly oscillatory second-order
The paper is concerned with what is sometimes called “intrinsic
oscillation’‘, namely originating in the structure of the differential
system itself, and as distinct to “extrinsic oscillation’‘, whereby the
oscillation is “pumped” into the system through an inhomogeneous term.
This is an important distinction, because the two forms of oscillation
are very different. In this paper, we address the highly oscillatory
second-order initial value problems of the first type by extending the
methods of the second. the asymptotic-numerical solvers for highly
oscillatory second-order problems are developed, the error bounds are
analyzed, and the accuracy is presented by numerical experiments.