Abstract: Classical finite difference schemes exhibit significant dispersion errors at medium-to-high wavenumbers. DRP (dispersion-relation-preserving) schemes mitigate these errors by optimizing phase accuracy in wavenumber space, while solution-adaptive schemes re-optimize stencil coefficients according to the evolving solution spectrum. However, frequent re-optimization incurs additional computational cost, and no criterion exists for selecting the interval. By exploiting the circulant structure of difference operators under periodic boundary conditions, this study reduces the cost of computing the statistics needed for optimization. A re-optimization strategy combining first-derivative truncation-error prediction with floating-point operation counts (FLOPs) is developed to determine the optimal interval for the proposed model. FLOPs can be estimated a priori, and their suitability as a cost metric is validated against measured runtime. Numerical results using a seven-point central difference scheme on three periodic nonlinear problems show that the proposed method significantly reduces errors at low additional computational cost.