Second order Chebyshev methods based on orthogonal polynomials

Numerische Mathematik

Volumn 90, Issue 1, 2001, Pages 1-18

  Abdulle, Assyr ^a   Medovikov, Alexei A ^b,c  

^a UNIVERSITY OF GENEVA   (Switzerland)

^b INSTITUTE OF NUMERICAL MATHEMATICS   (Russian Federation)

^c Kanda Software Inc   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035540065     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002110100292     Document Type: Article

References (19)

1. A. Abdulle: On roots and error constant of optimal stability polynomials. BIT 40, 177-182 (2000)
2. S.N. Bernstein: Sur les polynômes orthogonaux relatifs à un segment fini. J. Math. 9, 127-177 (1930)
3. E.B. Christoffel: Über die Gaussische Quadratur und eine Verallgemeinerung derselben. Journal für die reine und angewandte Mathematik 55, 61-82 (1858)
4. K. Gustafsson: Control-theoretic techniques for stepsize selection in implicit Runge-Kutta methods. ACM Trans. Math. Soft. 20, 496-517 (1994)
5. E. Hairer, S.P. Nørsett, G. Wanner: Solving Ordinary Differential Equations I. Nonstiff Problems, Springer Series in Comput. Math. 8, 2nd ed. Berlin: Springer, 1993
6. E. Hairer, G. Wanner: Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems, Springer Series in Comput. Math. 14, 2nd ed. Berlin: Springer, 1996
7. P.J. van der Houwen: Construction of integration formulas for initial value problems. Amsterdam: North-Holland, 1977
8. P.J van der Houwen, B.P. Sommeijer: On the internal stability of explicit m-stage Runge-Kutta methods for large m-values, Z. Angew. Math. Mech. 60, 479-485 (1980)
9. V.I. Lebedev: How to solve stiff systems of differential equations by explicit methods, Numerical Methods and Applications, pp. 45-80. Boca Raton: CRC Press, 1994
10. V.I. Lebedev: A new method for determining the zeros of polynomials of least deviation on a segment with weight and subject to additional conditions. Part I, Part II. Russian J. Numer. Anal. Math. Modelling. V. 8, N 3 (1993), pp. 195-222; V. 8, N 5 (1993), pp. 397-426
11. V.I. Lebedev: A new method for determining the zeros of polynomials of least deviation on a segment with weight and subject to additional conditions. Part I, Part II. Russian J. Numer. Anal. Math. Modelling. V. 8, N 3 (1993), pp. 195-222; V. 8, N 5 (1993), pp. 397-426
12. V.I. Lebedev: Zolotarev polynomials and extremum problems. Russian J. Numer. Anal. Math. Modelling, 9 (1994), pp. 231-263.
13. V.I. Lebedev, A.A. Medovikov: An explicit method of the second order of accuracy for solving stiff systems of ordinary differential equations. Russian Izv. Vyssh. Uchebn. Zaved. Mat. 9, 55-63 (1998)
14. A.A. Medovikov: High order explicit methods for parabolic equations. BIT 38, 372-390 (1998)
15. W. Riha: Optimal stability polynomials. Computing 9, 37-43 (1972)
16. B.P. Sommeijer, L.F. Shampine, J.G. Verwer: RKC: an explicit solver for parabolic PDEs. J. Comput. Appl. Math. 88, 316-326 (1998)
17. G. Szegö: Orthogonal Polynomials. New York: Amer. Math. Soc., 1939
18. J.W. Verwer: Explicit Runge-Kutta methods for parabolic partial differential equations. Runge-Kutta centennial. Appl. Num. Math. 22, 359-379 (1996)
19. H.A. Watts: Step size control in ordinary differential equation solvers. Trans. Soc. Computer Simulation 1, 15-25 (1984)