A family of efficient extrapolation formulae and their application in mechanics

The problem of extrapolation based just on a few initial terms of a sequence or series is discussed. Possible regularity of the extrapolation formula is postulated. Binomial power series is regarded as su ciently regular and several extrapolation formulae using 3, 4, or 5 initial terms and based on binomial power series are derived. They are called the `bs-extrapolation formulaeʹ and compared to other extrapolation algorithms. Good accuracy in many particular cases is stated. Three examples of applications in mechanics are quoted: they consider consecutive FEM-solutions, postbuckling behaviour of an Euler column and optimal plastic design of a plane T-head.