Abstract
Different kinds of approximation, especially chained approximation, are illustrated on linear and nonlinear differential equations. Particularly possibilities of getting exact error bounds are considered.
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References
E. Bredendiek, Charakterisierung und Eindeutigkeit bei simultanen Approximationen, Z. angew. Math. Mech. 50(1970), 403–410.
L. Collatz, The numerical treatment of differential equations, Springer 1960, 568 p.
L. Collatz, Über einige neue Entwicklungen bei Differenzenverfahren für Randwertaufgaben partieller Differentialgleichungen, Aplikace Matematiky, Prag, 10(1965), 165–177.
L. Collatz, Functional Analysis and Numerical Mathematics, Acad. Press 1966, 473 p.
L. Collatz, Einseitige Tschebyscheff Approximation bei Randwertaufgaben, Proc. Internat. Conference on Constructive funct. Theory, Varna, Bulgaria, 1970, 151–162.
L. Collatz, Hermitean methods for initial value problems in partial differential equations, to appear Proc. Symp. Numer. Methods, Dublin, Eire, 1972.
L. Collatz, Chained Approximation, to appear Proc. Symp. Funct. Anal. and Applicat., Madras, India, 1973.
L. Collatz — W. Krabs, Tschebyscheff Approximation, Teubner, 1973, to appear.
W. Krabs, Bemerkungen zur einseitigen Tschebyscheff Approximation, Computing 9(1972), 335–342.
P. J. Laurent, Approximation et optimisation, Paris 1972, 531 p.
A. R. Mitchell, Computational methods in partial differential equations, John Wiley & Sons, 1969, 255 p.
E. L. Wachspress, The ADI-Minimax problem, Proc. IFIP Congress, Edinburgh, 1968.
J. R. Whiteman, The mathematics of finite Elements and Applications, Acad. Press, 1973, 520 p.
J. R. Whiteman — J. A. Gregory, Mesh Refinement in Finite Element Methods, to appear, Proc. Symp. Numer. Solut. Diff. Equ., Dundee, 1973.
O. C. Zienkiewicz, The Finite Element Method in Engineering Science, McGraw Hill, 1971, 521 p.
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Collatz, L. (1974). Discretization and chained approximation. In: Watson, G.A. (eds) Conference on the Numerical Solution of Differential Equations. Lecture Notes in Mathematics, vol 363. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069123
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DOI: https://doi.org/10.1007/BFb0069123
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