On Turan type implicit Runge-Kutta methods

@article{Kastlunger1972OnTT,
  title={On Turan type implicit Runge-Kutta methods},
  author={K. H. Kastlunger and Gerhard Wanner},
  journal={Computing},
  year={1972},
  volume={9},
  pages={317-325}
}
Turan[5] has shown, that for a quadrature formula with multiple nodes $$\int\limits_{x_0 }^{x_0 + h} {f(t)dt\dot = h\sum {c_i^{(1)} } f(x_0 + b_i h) + h^2 \sum {c_i^{(2)} f'(x_0 + b_i h) + ... + h^m \sum {c_i^{(m)} } ^{f(m - 1)} (x_0 + b_i h)} } $$ there exist, form odd, “Gaussian” nodesb 1, ...,b s, so that the quadrature formula reaches order (m+1)s. In the present paper we show that these formulas can be extended to Implicit Runge-Kutta methods with multiple nodes (cf. [4]) also of order (m… CONTINUE READING

From This Paper

Figures, tables, and topics from this paper.

References

Publications referenced by this paper.
Showing 1-4 of 4 references

WANNER: Runge-Kutta Methods with Multiple Nodes

  • K. KASTLUNGER
  • Computing 9,
  • 1972
Highly Influential
3 Excerpts

On Pad6 Approximations to the Exponential Function and A-stable Methods for Num

  • B. EHLE
  • Sol. of Initial Value Prob.,
  • 1969

STANCU : Quadrature formulas with multiple Gaussian nodes

  • A. H. STROUD, D D.
  • J. SIAM Numer. Anal. B2,
  • 1965
2 Excerpts

On the theory of the mechanical quadrature

  • P. TURIN
  • Acta sci. math. 12A,
  • 1950
2 Excerpts

Similar Papers

Loading similar papers…