zbMATH — the first resource for mathematics

An operational approach to the Tau method for the numerical solution of non-linear differential equations. (English) Zbl 0449.65053

65L05 Numerical methods for initial value problems
65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
Full Text: DOI
[1] Fox, L., Parker, J. B.: Chebyshev polynomials in numerical analysis. Oxford: O. U. P. 1968. · Zbl 0153.17502
[2] Lanczos, C.: Trigonometric interpolation of empirical and analytical functions. J. Math. Phys.17, 123–139 (1938). · Zbl 0020.01301
[3] Luke, Y.: The special functions and their approximations, Vol. II. New York: Academic Press 1969. · Zbl 0193.01701
[4] Ortiz, E. L.: On the generation of the canonical polynomials associated with certain linear differential operators. Imperial College Res. Rep., 1–22 (1964).
[5] Ortiz, E. L.: The Tau method. SIAM J. Numer. Anal.6, 480–492 (1969). · Zbl 0195.45701 · doi:10.1137/0706044
[6] Ortiz, E. L.: Sur quelques nouvelles applications de la Méthode Tau. Seminaire Lions, Analyse et Contrôle de Systèmes, IRIA, Paris, 247–257 (1975).
[7] Ortiz, E. L.: Step by step Tau method. Part I: Piecewise polynomial approximations. Comp. and Math. Appl.1, 381–392 (1975). · Zbl 0356.65006 · doi:10.1016/0898-1221(75)90040-1
[8] Ortiz, E. L.: On the numerical solution of non-linear and functional differential equations with the Tau method. In: Numerical treatment of differential equations in applications (Ansorge, R., Törnig, W., Hrsg.), S. 127–139. Berlin-Heidelberg-New York: Springer 1978.
[9] Ortiz, E. L., Purser, W. F. C., Rodriguez Cañizarez, F. J.: Automation of the Tau method. Imperial College Res. Rep., 1–58. Presented at the Conference on Numerical Analysis, Royal Irish Academy, Dublin, 1972.
[10] Ortiz, E. L., Pham, A.: On the convergence of the non-linear formulation of the Tau method. (To appear elsewhere.)
[11] Ortiz, E. L., Samara, H.: Polynomial methods for differential eigenvalue problems. Imperial College Res. Rep. 1-36 (1978).
[12] Ortiz, E. L., Samara, H.: Some equivalence results concerning a class of polynomial methods for the numerical solution of differential equations. Imperial College Res. Rep., 1–34 (1978).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.