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Contribution to error estimate. (English) Zbl 0512.34011

MSC:

34A45 Theoretical approximation of solutions to ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
41A25 Rate of convergence, degree of approximation
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References:

[1] Finlayson, B. A., The Method of Weighted Residuals and Variational Principles (1972), Academic Press: Academic Press New York · Zbl 0319.49020
[2] Churchill, R. V., Fourier Series and Boundary Value Problems (1969), McGraw-Hill: McGraw-Hill New York · Zbl 0025.05403
[3] Collatz, L., Eigenvertaufgaben mit Technischen Anwendungen (1963), Akad. Verlagsgesellschaft: Akad. Verlagsgesellschaft Leipzig
[4] Ciarlet, P. G.; Schultz, M. H.; Varga, R. S., Numerical methods of high-order accuracy for nonlinear boundary value problems, Numer. Math., 9, 394-430 (1967) · Zbl 0155.20403
[5] Arthurs, A. M., Complementary Variational Principles (1970), Oxford Univ. Press (Clarendon): Oxford Univ. Press (Clarendon) London/New York · Zbl 0202.38404
[6] Anderson, N.; Arthurs, A. M., Extremum principles and error bounds for a nonlinear singular-boundary value problem in the theory of viscous fluids, Lett. Nuovo Cimento, 3, 13, 562-566 (1972)
[7] Arthurs, A. M., Dual extremum principles and error bounds for a class of boundary value problems, J. Math. Anal. Appl., 41, 3, 781-795 (1973) · Zbl 0251.35049
[8] Djukic, Dj. S.; Atanackovic, T. M., Error bounds via a new extremum variational principles, mean-square residual and weighted mean̄square residual, J. Math. Anal. Appl., 75, 203-218 (1980) · Zbl 0429.65083
[9] Vujanovic, B., On one variational principle for irreversible phenomena, Acta Mech., 19, 259 (1974)
[10] Vujanovic, B.; Atanackovic, T., On the use of Jourdain’s variational principle in nonlinear mechanics and transport phenomena, Acta Mech., 29, 229 (1978) · Zbl 0395.70018
[11] Markus, L.; Amundson, N. R., Nonlinear boundary-value problems arising in chemical reactor theory, J. Differential Equations, 4, 102 (1968) · Zbl 0155.13301
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