Romberg Integration is a numerical technique for estimating definite integrals by combining the trapezoidal rule with Richardson extrapolation, leading to increased accuracy by systematically eliminating error terms. It is particularly useful for integrating functions that are smooth and well-behaved over the interval of integration, offering a balance between computational efficiency and precision.
Diffusion of Innovations is a theory that seeks to explain how, why, and at what rate new ideas and technology spread through cultures. It identifies the stages of adoption over time and the roles of different participants in the diffusion process, from innovators to laggards.