The stability properties ofq-step backward difference schemes
- 56 Downloads
We present a new proof that aq-step backward difference scheme for the approximate solution of a first order ordinary differential equation is stable in the sense of Dahlquist iff 1≦q≦6.
The only other proof known to the authors was given by Cryer in a condensed version with most proofs omitted of a much larger technical report.
KeywordsDifferential Equation Ordinary Differential Equation Approximate Solution Computational Mathematic Difference Scheme
Unable to display preview. Download preview PDF.
- 1.David M. Creedon and John J. H. Miller,The Stability Properties of q-step backward difference schemes, Rep. No. TCD 1974–7. School of Maths., Trinity College, Dublin (1974), 1–11.Google Scholar
- 2.Colin W. Cryer,A proof of the instability of backward-difference multistep methods for the numerical integration of ordinary differential equations, Tech. Rep. No. 117, Comp. Sci. Dept., Univ. of Wisconsin, Madison (1971), 1–52.Google Scholar
- 4.John J. H. Miller,On the location of zeros of certain classes of polynomials with applications to numerical analysis, J. Inst. Math. Applic. 8 (1971), 397–406.Google Scholar
- 5.John J. H. Miller,On weak stability, stability and the type of a polynomial, Lecture Notes in Mathematics Vol. 228, Ed. John Ll. Morris, Springer-Verlag (1971), 316–320.Google Scholar
- 6.John J. H. Miller,Practical algorithms for finding the type of a polynomial, Studies in Numerical Analysis, Ed. B. K. P. Scaife, Academic Press (1974), 253–264.Google Scholar
- 7.D. P. McCarthy and John J. H. Miller,The refinement and implementation of an algorithm for finding the type of a polynomial, Séminaires Analyse Numérique, J. L. Lions, P. A. Raviart, Université Paris VI (1972/73).Google Scholar
- 8.John J. H. Miller,On the type of a polynomial relative to a circle — an open problem, Optimization Techniques, IFIP Tech. Conf., Novosibirsk, July 1974. Ed. G. I. Marchuk, Lecture Notes in Computer Science No. 27, Springer-Verlag (1975), 394–399.Google Scholar