Numerical methods based on polynomial spline interpolation
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.
KeywordsCoarse Grid Hermite Formulation Spline Approximation Large Reynolds Number Polynomial Spline
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