Oscillation-free solutions to Volterra integral and integro-differential equations with periodic force terms

Volterra equations governed by oscillatory functions arise frequently in applied fields. To construct efficient algorithms for solving these equations, oscillatory properties of their solutions should be studied. In this paper, oscillatory orders of solutions to a class of highly oscillatory Volterra integral equations are presented. Then some modified solutions are given with the help of asymptotic expansions of highly oscillatory integrals. Finally, theoretical analysis verifies these modified solutions enjoy less oscillation than the original one, and extensions to highly oscillatory Volterra integro-differential equations are considered.