In this talk we develop a method for efficient computation of reduced-order nonlinear solutions (RONS). RONS is a framework to create reduced-order models for time-dependent partial differential equations (PDEs) where the reduced-order solution has nonlinear dependence on time-varying parameters. With RONS we obtain an explicit set of ordinary differential equations (ODEs) to evolve the parameters. These ODEs minimize the instantaneous error between dynamics of the governing PDE and dynamics of the reduced-order solution. Additionally, we can easily enforce conserved quantities of the PDE in the reduced solution using the RONS framework. The main computational cost of RONS comes from calculating integrals to form the reduced-order equations, which is computationally expensive when the reduced-order model depends on many parameters. By exploiting the structure of the RONS equations and using symbolic computation, we significantly reduce the computational cost of calculating these integrals. This allows us to apply RONS to systems with complex dynamics.