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Numerical methods of high-order accuracy for singular nonlinear boundary value problems. (English) Zbl 0211.19103

65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
65N15Error bounds (BVP of PDE)
Full Text: DOI EuDML
[1] Ciarlet, P. G.: AnO(h 2) method for a non-smooth boundary value problem. Acquat. Math.2, 39--49 (1968). · Zbl 0159.11703 · doi:10.1007/BF01833489
[2] ----, Schultz, M. H., Varga, R. S.: Numerical methods of high-order accuracy for nonlinear boundary value problems. I. One dimensional problem. Numer. Math.9, 394--430 (1967). · Zbl 0155.20403 · doi:10.1007/BF02162155
[3] ----: Numerical methods of high-order accuracy for nonlinear two-point boundary value problems. Programmation en Mathématiques Numériques (Proceedings of the International Colloquium C.N.R.S., Besançon, France, Sept. 7--14, 1966), pp. 217--225. Paris: C.N.R.S. 1968.
[4] ----: Numerical methods of high-order accuracy for nonlinear boundary value problems. V. Monotone operator theory. Numer. Math.13, 51--77 (1969) · Zbl 0181.18603 · doi:10.1007/BF02165273
[5] Gusman, Yu. A., Oganesyan, L. A.: Inequalities for the convergence of finite difference schemes for degenerate elliptic equations. Z. Vycisl. Mat. i Mat. Fiz.5, 351--357 (1965)
[6] Jamet, P.: Numerical methods and existence theorems for singular linear boundary-value problems. Doctoral Thesis, University of Wisconsin, 1967 · Zbl 0161.35804
[7] ----: On the convergence of finite-difference approximations to one-dimensional singular boundary-value problems. Numer. Math.14, 355--378 (1970) · Zbl 0179.22103 · doi:10.1007/BF02165591
[8] Neoas, J.: Les Méthodes Directes en Théorie des Equations Elliptiques. Paris: Masson 1967. (351 pp.)
[9] Parter, S. V.: Numerical methods for generalized axially symmetric potentials. J. Soc. Indust. Appl. Math. Ser. B Numer. Anal.2, 500--516 (1965) · Zbl 0137.33402 · doi:10.1137/0702040
[10] Perrin, F. M., Price, H. S., Varga, R. S.: On higher-order numerical methods for nonlinear two-point boundary value problems. Numer. Math.13, 180--198 (1969). · Zbl 0183.44501 · doi:10.1007/BF02163236