Two-step methods and bi-orthogonality
Authors: A. Iserles and S. P. Nørsett
Journal: Math. Comp. 49 (1987), 543-552
MSC: Primary 65L05; Secondary 33A65
MathSciNet review: 906187
Abstract: We study order and zero-stability of two-step methods of Obrechkoff type for ordinary differential equations. A relation between order and properties of mth degree polynomials orthogonal to , , where , is established. These polynomials are investigated, focusing on their explicit form, Rodrigues-type formulae and loci of their zeros.
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- A. Iserles, "Two-step numerical methods for parabolic differential equations," BIT, v. 21, 1981, pp. 80-96. MR 616702 (83i:65065)
- A. Iserles & S. P. Nørsett, "Bi-orthogonal polynomials," in Orthogonal Polynomials and Their Applications (A. Draux, A. Magnus and P. Maroni, eds.), Lecture Notes in Math., vol. 1171, Springer-Verlag, Berlin, 1985, pp. 92-100. MR 838964 (87f:00023)
- A. Iserles & S. P. Nørsett, On the Theory of Bi-Orthogonal Polynomials, Tech. Rep. NA1, DAMTP, University of Cambridge, 1986.
- S. P. Nørsett, "One-step methods of Hermite type for numerical integration of stiff systems," BIT, v. 14, 1974, pp. 63-77. MR 0337014 (49:1787)
- S. P. Nørsett, "Splines and collocation for ordinary initial value problems," in Approximation Theory and Spline Functions (S. P. Singh, J. H. W. Burry and B. Watson, eds.), NATO ASI Series, Vol. C136, 1983, pp. 397-417. MR 786857 (86j:41008)
- R. E. Shafer, "On quadratic approximation," SIAM J. Numer. Anal., v. 7, 1974, pp. 447-460. MR 0358161 (50:10626)
- G. Wanner, E. Hairer & S. P. Nørsett, "Order stars and stability theorems," BIT, v. 18, 1978, pp. 475-489. MR 520756 (81b:65070)