×

zbMATH — the first resource for mathematics

On the existence of solutions to the algebraic equations in implicit Runge-Kutta methods. (English) Zbl 0506.65030

MSC:
65L05 Numerical methods for initial value problems involving ordinary differential equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] K. Burrage and J. C. Butcher,Stability criteria for implicit Runge-Kutta methods, SIAM J. Numer. Anal. 16 (1979), 46–57. · Zbl 0396.65043
[2] M. Crouzeix, Sur la B-stabilité des méthodes de Runge-Kutta, Numer. Math. 32 (1979), 75–82. · Zbl 0431.65052
[3] M. Crouzeix and P. A. Raviart, Unpublished Lecture Notes, Université de Rennes 1980.
[4] G. Dahlquist,Error analysis for a class of methods for stiff nonlinear initial value problems, Lecture Notes in Mathematics 506, Berlin, Springer-Verlag (1976). · Zbl 0352.65042
[5] G. Dahlquist and R. Jeltsch,Generalized disks of contractivity for explicit and implicit Runge-Kutta methods. Report TRITA-NA-7906, Dept. Comp. Sci., Roy. Inst. of Techn., Stockholm (1979). · Zbl 1106.65062
[6] C. A. Desoer and H. Haneda,The measure of a matrix as a tool to analyse computer algorithms for circuit analysis. IEEE Trans. Circuit Theory 19 (1972), 480–486.
[7] H. Gajewski, K. Gröger and K. Zacharias,Nichtlineare Operatorgleichungen und Operator-differentialgleichungen, Berlin, Akademie-Verlag (1974). · Zbl 0289.47029
[8] J. M. Ortega and W. C. Rheinboldt,Iterative Solution of Nonlinear Equations in Several Variables, New York, Academic Press (1970). · Zbl 0241.65046
[9] I. W. Sandberg,Theorems on the computation of transient response of nonlinear networks containing transistors and diodes, Bell System Tech. J. 49 (1970), 1739–1776. · Zbl 0221.94047
[10] I. W. Sandberg and H. Shichman,Numerical integration of systems of stiff nonlinear differential equations, Bell System Tech. J. 47 (1968), 511–527. · Zbl 0221.65128
[11] J. Williams,The problem of implicit formulas in numerical methods for stiff differential equations, Numer. Anal. Report No. 40, Depth. of Math., University of Manchester, Manchester (1979).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.