-stability and dominating pairs
Abstract: It is considered whether linear combinations of A-acceptable exponential approximations preserve the A-stability, when the coefficients of the linear combination are selected in order to achieve exponential fitting. Various pairs of exponential approximations are discussed and the satisfactory pairs are characterized.
-  Byron L. Ehle, 𝐴-stable methods and Padé approximations to the exponential, SIAM J. Math. Anal. 4 (1973), 671–680. MR 331787, https://doi.org/10.1137/0504057
-  B. EHLE, Some Results on Exponential Approximation and Stiff Equations, Univ. of Victoria Res. Rep. #77, Victoria, B.C., Canada, 1974.
-  Byron L. Ehle and Zdenek Picel, Two-parameter, arbitrary order, exponential approximations for stiff equations, Math. Comp. 29 (1975), 501–511. MR 375737, https://doi.org/10.1090/S0025-5718-1975-0375737-7
-  Arieh Iserles, Functional fitting–new family of schemes for integration of stiff O.D.E, Math. Comp. 31 (1977), no. 137, 112–123. MR 431688, https://doi.org/10.1090/S0025-5718-1977-0431688-2
-  Leon Lapidus and John H. Seinfeld, Numerical solution of ordinary differential equations, Mathematics in Science and Engineering, Vol. 74, Academic Press, New York-London, 1971. MR 0281355
-  Syvert P. Nørsett, 𝐶-polynomials for rational approximation to the exponential function, Numer. Math. 25 (1975/76), no. 1, 39–56. MR 410189, https://doi.org/10.1007/BF01419527
- B. EHLE, "A-stable methods and Padé approximations to the exponential," SIAM J. Math. Anal., v. 4, 1973, pp. 671-680. MR 0331787 (48:10119)
- B. EHLE, Some Results on Exponential Approximation and Stiff Equations, Univ. of Victoria Res. Rep. #77, Victoria, B.C., Canada, 1974.
- B. EHLE &. Z. PICEL, "Two-parameter, arbitrary order, exponential approximations for stiff equations," Math. Comp., v. 29, 1975, pp. 501-511. MR 0375737 (51:11927)
- A. ISERLES, "Functional fitting-New family of schemes for integration of stiff O.D.E.," Math. Comp., v. 31, 1977, pp. 112-123. MR 0431688 (55:4683)
- L. LAPIDUS & J. H. SEINFELD, Numerical Solution of Ordinary Differential Equations, Academic Press, New York, 1971. MR 0281355 (43:7073)
- S. P. NØRSETT, "C-polynomials for rational approximation to the exponential function," Numer. Math., v. 25, 1975, pp. 39-56. MR 0410189 (53:13939)
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