Computation of the M matrix for fourth-order problems

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 452, Issue 1951, 1996, Pages 1765-1788

  Bennewitz, C ^a   Brown, B M ^b   Evans, W D ^b   McCormack, D K R M ^b   Marletta, M ^c  

^a LUND UNIVERSITY   (Sweden)

^b CARDIFF UNIVERSITY   (United Kingdom)

^c UNIVERSITY OF LEICESTER   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0010666028     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.1996.0094     Document Type: Article

References (29)

1. Atkison, F. V. 1964 Discrete and continuous boundary problems. New York: Academic. Bellman, R. E., Kagiwada, H. H. & Kalaba, R. E. 1967 Invariant imbedding and the numerical integration of boundary-value equations. Commun. ACM W, 100-102
2. . Bennewitz, C. \V. 1984 A general version of the Hardy-Littlewood-Polya-Everitt (HELP) inequality. Proc. R. Soc. Edinb. A 97, 9-20.
3. Bennewitz, C. \V. & Everitt, W. N. 1980 Some remarks on the Titchmarsh-Weyl m-coefficient. In Proc. of the Pleijel Conf. (Uppsala).
4. Brown, B. M. & Evans, W. D. 1973 On the limit-point and strong limit-point classification of 2nth order differential expressions with widely oscillating coefficients. Math. Z. 134, 351-368.
5. Brown, B. M., Evans, W. D. & Everitt, W. N. 1990 HELP integral and series inequalities. In Proc. of the VI meeting on General Inequalities (Oberwolfach 1990). (International Series of Numerical Mathematics 103) (ed. W. Walter), pp. 269-305.
6. Brown, B. M., Evans, W. D., Everitt, W. N. & Kirby, V. G. 1994a Two integral inequalities, vol. 3. Singapore: World Scientific.
7. Brown, B. M., Evans, W. D. & Kirby, V. G. 19946 A numerical investigation of HELP inequalities. Res. Math. 25, 20-39.
8. Brown, B. M., Kirby, V. G. & Pryce, J. D. 1989 Numerical determination of the TitchmarshWeyl m-coefficient and its applications to HELP inequalities. Proc. R. Soc. Lond. A 426, 167-188.
9. Brown, B. M., Kirby, V. G. & Pryce, J. D. 1991 A numerical method for the determination of the Titchmarsh-Weyl m-coefficient. Proc. R. Soc. Lond. A 435, 535-549.
10. Chaudhuri, J. & Everitt, W. N. 1968 On the spectrum of ordinary second order differential operators. Proc. R. Soc. Edinb. A 68, 95-119.
11. Coppel, W. A. 1971 Disconjugacy. (Lecture Notes in Mathematics 220). Berlin: Springer.
12. Delfour, M. C. & Ouansafi, A. 1992 Noniterative approximations to the solution of the matrix Riccati differential equation. SIAM Jl Numer. Analysis 29, 1648-1693.
13. Dias, N. G. J. 1994 On an integral inequality associated with a 2nth order quasi-differential expression. Ph.D. thesis, University of Wales, Cardiff.
14. Evans, W. D. &: Everitt, W. N. 1982 A return to the Hardy-Littlewood inequality. Proc. R. Soc. Land. A 380, 447-486.
15. Everitt, W. N. 1963 Fourth order singular differential equations. Math. Annln 149, 320-340.
16. Everitt, W. N. 1989 On an extension to an integro-differential inequality of Hardy, Littlewood and Pölya. Proc. R. Soc. Edinb. A 69, 295-333.
17. Greenberg, L. & Marietta, M. 1996 The SLEUTH software package for fourth order SturmLiouville problems. SIAM Jl Sei. Stat. Comp. (Submitted.)
18. Hinton, D. B. & Shaw, J. K. 1981a Titchmarsh-Weyl theory for Hamiltonian systems. In Spectral theory of differential operators (ed. I. W. Knowles & R. T. Lewis), pp. 219-231. Amsterdam: North-Holland.
19. Hinton, D. B. & Shaw, J. K. 19816 On Titchmarsh-Weyl m(A)-functions for Hamiltonian systems. J. Diffl Equal. 40, 316-342.
20. Hinton, D. B. & Shaw, J. K. 1982 On the spectrum of a singular Hamiltonian system. Quaestiones Mathematicae 5, 29-81.
21. Krall, A. M. 1989 m(A) theory for singular Hamiltonian systems with one singular point. SIAM Jl Math. Analysis 20, 664-700.
22. Kuki, H. 1972 Complex gamma function with error control. Commun. ACM. 15, 262-267.
23. Naimark, M. A. 1968 Linear differential operators, vol. 2. New York: Ungar.
24. Nelson, P. 1972 A comparative study of invariant imbedding and superposition. Int. Jl Comput. Math. B 3, 195-207.
25. Russell, A. 1975 Integral inequalities and spectral theory of certain ordinary differential operators. Ph.D. thesis, University of Dundee.
26. Russell, A. 1989a On a certain fourth-order integral inequalities. Proc. R. Soc. Edinb. A 83, 205-211.
27. Russell, A. 1989& On a fourth-order singular integral inequality. Proc. R. Soc. Edinb. A 80, 249-260.
28. Thompson, I. J. & Barnett, A. R. 1987 Modified Bessel functions iv(z) and kv(z) of real order and complex argument, to selected accuracy. Comput. Phys. Comm. 47, 245-257.
29. Titchmarsh, E. C. 1962 Eigenfunction expansions, part 1, 2nd edn. Oxford University Press. Weyl, H. 1910 Über gewöhnliche Differentialgleichungen mit Singularitäten und die zugehörigen Entwicklungen willkürlicher Punktionen. Math. Annln. 68, 220-269.