Numerical methods based on polynomial spline interpolation

  • S. G. Rubin
  • P. K. Khosla
Part of the Lecture Notes in Physics book series (LNP, volume 59)


Polynomial spline interpolation has been used to develop a variety of higher-order collocation methods. Only those polynomials resulting in tridiagonal, or at worst 3×3 block- tridiagonal, matrix systems have been evaluated.It is- shown that the Padé or Hermite formulation is a hybrid method resulting from two different poly nomial splines.An extension to sixth-order is presented in this paper. Of the fourth-order methods, Spline 4(5,6 has the smallest truncation error. The sixth-order Hermite formulation leads to extraordinary accuracy even with very coarse grids.

An important conclusion of the present study is that, for equal accuracy, the Spline 4 procedure requires one-fourth as many points, in a given direction, as a finite-difference calculation. This means less computer time and storage. Also, divergence form is preferable for coarse grids and/or large Reynolds numbers.


Coarse Grid Hermite Formulation Spline Approximation Large Reynolds Number Polynomial Spline 
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Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • S. G. Rubin
    • 1
  • P. K. Khosla
    • 1
  1. 1.Polytechnic Institute of New YorkFarmingdale

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