## A class of $$A$$-stable methods.(English)Zbl 0208.41504

### MSC:

 65L05 Numerical methods for initial value problems involving ordinary differential equations 65L20 Stability and convergence of numerical methods for ordinary differential equations
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### References:

 [1] O. Axelsson,Global integration of differential equations through Lobatto quadrature, BIT 4 (1964), 69–86. · Zbl 0122.12204 [2] R. Bellman,Stability theory of differential equations, McGraw-Hill, New York-Toronto-London, 1953. · Zbl 0053.24705 [3] G. Birkhoff and R. S. Varga,Discretization errors for well-set Cauchy Problems. I, Journal of Math. and Physics, 45 (1965), 1–23. · Zbl 0134.13406 [4] G. Dahlquist,A special stability problem for linear multistep methods, BIT 3 (1963), 27–43. · Zbl 0123.11703 [5] F. R. Gantmacher,Matrizenrechnung II, VEB Deutscher Verlag der Wissenschaften, Berlin, 1959. [6] C. W. Gear,The automatic integration of stiff ordinary differential equations, IFIP Congress, Edinburgh, 1968. [7] P. Henrici,Error propagation for difference methods, John Wiley & Sons, Inc., New York, London, 1962. · Zbl 0171.36104 [8] P. M. Hummel and C. L. Seebeck,A generalization of Taylor’s theorem, Amer. Math. Monthly, 56 (1949), 243–247. · Zbl 0037.17601 [9] T. E. Hull,The numerical integration of ordinary differential equations, IFIP Congress, Edinburgh, 1968. [10] M. Marden,Geometry of polynomials, Mathematical Surveys No 3, American Mathematical Society, Providence, Rhode Island, 1966. · Zbl 0162.37101 [11] O. Perron,Die Lehre von den Kettenbrüchen, Chelsea Publ. Comp., New York, 1950. · Zbl 0041.18206 [12] J. Shohat,On mechanical quadratures, in particular with positive coefficients, Trans. Amer. Math. Soc. 42, 1937, 461–496. · JFM 63.0960.02 [13] M. H. Schultz,Difference methods for Cauchy problems in S’*, Journal of Math. and Mech. 16 (1967), 1117–1129. · Zbl 0146.33204 [14] R. S. Varga,On higher order stable implicit methods for solving parabolic partial differential equations, Journal of Math. and Physics, 40 (1961), 220–231. · Zbl 0106.10805 [15] O. Widlund,A note on unconditionally stable linear multistep methods, BIT 7 (1967), 65–70. · Zbl 0178.18502
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