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On the a-posteriori error bounds for the solution of ordinary nonlinear differential equations. (English) Zbl 0382.65033

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
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[1] Henrici, P., (Discrete Variable Methods in Ordinary Differential Equations (1962), V. Wiley: V. Wiley New York), Chapters III · Zbl 0112.34901
[2] Ralston, A.; Wilf, H., (Mathematical Methods for Digital Computers (1960), Wiley: Wiley New York), Chapter IV · Zbl 0089.12602
[3] Todd, J., (Survey of Numerical Analysis (1962), McGraw-Hill: McGraw-Hill New York), Chapter IX · Zbl 0101.33601
[4] Stroem, T., Absolutely monotonic majorants and their use for automatic strict error estimation in some areas of numerical analysis, (Report of Royal Inst. Tech. (Feb. 1971), Stockholm: Stockholm Sweden)
[5] Lepshin, E. A., Statistical investigation of random errors in numerical solutions of ordinary differential equations, USSR Computer Math and Math Physics (1972)
[6] Tal, A. A., The numerical solution of the radiative transfer function, (Technical Report 67-55 (Nov. 1967), Univ. of Maryland, Computer Center)
[7] Gutkenecht, M., A-posteriori error bounds for the zeros of a polynomial, Numer. Math., 20, 139 (1973)
[8] Gladwell, I., A-posteriori error bounds for approximate solution of linear second-order differential equations, J. Inst. Math. Appls, 9, 3, 323 (1972) · Zbl 0236.65057
[9] Collatz, L., (Functional Analysis and Numerical Mathematics (1966), Academic Press: Academic Press New York), Chapter III · Zbl 0221.65088
[10] Henrici, P., (Elements of Numerical Analysis (1964), Wiley: Wiley New York), Chapter XIV · Zbl 0149.10901
[11] Ince, E. L., (Ordinary Differential Equations (1956), Dover Publications: Dover Publications London), Chapter III · JFM 53.0399.07
[12] Geisler, E. G., Integration and error estimation in dynamical systems, (M.Sc. Thesis (1970), Faculty of E. E.: Faculty of E. E. Technion I.I.T.)
[13] Stiefel, E. L., (An Introduction to Numerical Mathematics (1963), Academic Press: Academic Press New York), Chapter VI · Zbl 0154.16702
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