What Is convergence acceleration anyway?

The concept of convergence acceleration is presented through two examples of its application to very different physics. The first is for self-assembly of misfolded proteins described by moments of the filament length distribution. With convergence acceleration, highly accurate moments can be found, as confirmed by a manufactured solution, leading to a more accurate estimate of spongiform disease onset. The second application considers the transient behavior of a nuclear reactor. Here, the reactor kinetics equations (RKE) are solved to extreme accuracy as demonstrated by comparison to analytical and manufactured solutions. From our investigation, we conclude that with some added initiative and effort, extreme accuracy in a numerical computation involving discretization is achievable through convergence acceleration.