Derivations of Point-2 and Point-3 Time-Sequence Extrapolation Formulas

As noted, a problem of existing extrapolation formulas is that only the first unknown point after the known time sequence is extrapolated. Thus, new and efficient multiple-point extrapolation formulas are needed to be derived. In this paper, Lagrange interpolation polynomials are presented to derive the point-2 and point-3 time-sequence extrapolation formulas. Numerical experiments are carried out to validate the formulas, and the results are satisfactory. As shown, the point-2 and point-3 time-sequence extrapolation formulas are effective to approximate a continuous smooth function.