Numerical Verification of Subharmonic Solutions in the Ikeda Delay Differential Equation with External Force Term

Abstract

Abstract. We perform numerical verification of subharmonic solutions in the Ikeda delay differential equation with an external force term, a model for optical resonance systems. The Ikeda delay differential equation treated in this paper is characterized by the inclusion of trigonometric functions as nonlinear terms, and conventional numerical verification method, which are effective when the nonlinear terms are of polynomial type, cannot be applied as is. Therefore, we treat the nonlinear terms by numerical integration using the Euler-Maclaurin formula for numerical verification.