Two-point padé approximants to stieltjes series representation of bulk moduli of regular composites

Computer Assisted Mechanics and Engineering Sciences

Volumn 3, Issue 2, 1996, Pages 121-132

  Tokarzewski, Stanislaw ^a   Telega, Józef Joachim ^a  

^a INSTITUTE OF FUNDAMENTAL TECHNOLOGICAL RESEARCH   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; BOUNDARY CONDITIONS; CONVERGENCE OF NUMERICAL METHODS; MATHEMATICAL MODELS;

SQUARE ARRAY; TRANSPORT COEFFICIENTS; TWO PHASE COMPOSITE MATERIALS; TWO POINT PADE APPROXIMANTS;

COMPOSITE MATERIALS;

EID: 0029720230     PISSN: 1232308X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (24)

1. G.A. Baker. Essentials of Padé Approximants. Acad. Press, London, 1975.
2. G.A. Baker, P. Graves-Morris. Padé Approximants. Part I: Basic Theory. Encyclopedia of Mathematics and its Applications, 13, Addison-Wesley Publ. Co., London, 1981.
3. G.A. Baker, P. Graves-Morris. Padé Approximants, Part II: Extensions and Applications. Encyclopedia of Mathematics and its Applications, 14, Addison-Wesley Publ. Co., London, 1981.
4. D.J. Bergman. The dielectric constant of a composite material - A problem in classical physics, Phys. Report., C 43: 377-407, 1978.
5. A. Bultheel. Laurent Series and their Padé Approximants. Birkhäuser-Verlag, Basel, 1987.
6. L. Casasús, P. González-Vera. Two-point Padé type approximants for Stieltjes functions. In: C. Brezinski, A. Draux, A.P. Magnus, P. Moroni and A. Ronveaux, eds. Proc. Polinômes Ortogonaux et Applications, Bar-le-Duc 1984, Lecture Notes in Math., 1171: 408-418, Springer, Berlin, 1985.
7. J. Gilewicz. Approximants de Padé. Springer-Verlag, Berlin, 1978.
8. P. Gonzalez-Vera, O. Njåstad. Convergence of two-point Padé approximants to series of Stieltjes. J. Comp. Appl. Math., 32: 97-105, 1990.
9. W.B. Gragg. Truncation error bounds for T-fractions. In: E.W. Cheney, ed. Approximation Theory III, 455-460, Academic Press, New York, 1980.
10. W.B. Jones, O. Njåstad, W.J. Thron. Two-point Padé expansions for a family of analytic functions. J. Comp. Appl. Math., 9: 105-123, 1983.
11. W.B. Jones, W.J. Thron. A posteriori bound for truncation error of continued fraction. SIAM J. Num. Anal., 8: 693-705, 1970.
12. W.B. Jones, W.J. Thron. Continued Fraction Analytic Theory and its Applications. Encyclopedia of Mathematics and its Applications, 11, Addison-Wesley Publ. Co., London, 1980.
13. S. May, S. Tokarzewski, A. Zachara, B. Cichocki. Continued fraction representation for the effective thermal conductivity coefficient of a periodic two component composite. Int. J. of Heat and Mass Transf., 37: 2165-2173, 1994.
14. R.C. McPhedran, G.W. Milton. Bounds and exact theories for the transport properties of inhomogeneous media. Appl. Phys. A, 207-220, 1981.
15. R.C. McPhedran, L. Poladian, G.W. Milton. Asymptotic studies of closely spaced highly conducting cylinders. Proc. R. Soc. London A, 415: 185-196, 1988.
16. S. Tokarzewski. Inequalities for the effective transport coefficients. Arch. Mech., 46: 611-623, 1994.
17. S. Tokarzewski. Two-point Padé approximants for the expansions of Stieltjes functions in real domain. J. Comp. Appl. Math., 1995 (in press).
18. S. Tokarzewski, J. Blawzdziewicz, I.V. Andrianov. Two-point Padé approximants for Stieltjes series, IFTR Reports, 30/1993.
19. S. Tokarzewski, J. Blawzdziewicz, I.V. Andrianov. Effective conductivity of densely packed highly conducting cylinders. Appl. Phys., A 59: 601-604, 1994.
20. S. Tokarzewski, J. Blawzdziewicz, I.V. Andrianov. Two-point Padé approximants for formal Stieltjes series. Num. Algorithms, 8: 313-328, 1994.
21. S. Tokarzewski, J.J. Telega. S-continued fraction representation for effective transport coefficients of two-phase media, IFTR Reports, 16/95.
22. S. Tokarzewski, J.J. Telega. Inequalities for two-point Padé approximants to the expansions of Stieltjes functions in real domain (submitted).
23. S. Tokarzewski, J.J. Telega. S-continued fraction bounds for real effective moduli of two-phase composite materials (submitted).
24. H.S. Wall. Analytic Theory of Continued Fractions. New York, Van Nostrand, 1948.