Abstract
In this paper optimal order, k-step methods with one nonstep point for the numerical solution of y' = f(x,y) y(a) = n, introduced by Gragg and Stetter (1) are extended to an arbitrary number s of nonstep points. These methods have order 2k + 2s, are proved stable for k ≤ 8, s ≥ 2, and not stable for large k.
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References
Gragg, W.B., and Stetter, H.J., Generalized multistep predictor-corrector methods, J.ACM 11(1964), 188–209.
Danchick, R., Further results on generalized predictor-corrector methods. J.COMP.A.SYST.SCIEN. 2(1968), 203–218.
Marden, M., Geometry of polynomials. American mathematical society, Providence, Rhode Island, 1966.
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Lyche, T. (1969). Optimal order multistep methods with an arbitrary number of nonsteppoints. In: Morris, J.L. (eds) Conference on the Numerical Solution of Differential Equations. Lecture Notes in Mathematics, vol 109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0060028
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DOI: https://doi.org/10.1007/BFb0060028
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