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The authors show on simple experimental examples the unsatisfactory properties of the simple and frequently used method of combination of solutions in comparison with the factorization method. The results obtained are in accordance with the theoretical analysis of the numerical processes in question which was given in other papers.
[1] Ivo Babuška, Milan Práger, Emil Vitásek: Numerical Processes in Differential Equations. John Wiley & Sons, London-New York-Sydney; SNTL Praha (1966). MR 0223101
[2] Ivo Babuška: Numerical Stability in Mathematical Analysis. IFIP Congress 68, Invited papers, 1-13 (1968). MR 0235725
[3] Jiří Taufer: On Factorization Method. Aplikace matem. 11, 6, 427-451 (1966). MR 0226872
[4] Jiří Taufer: Faktorisierungsmethode für ein Randwertproblem eines linearen Systems von Differential Gleichungen. Aplikace matem. 13, 2, 191 - 198 (1968). MR 0231542
[5] Jiří Taufer: Lösung der Randwertprobleme für Systeme von linearen Differentialgleichungen. In print. (1968).
[6] T. J. Dekker: A floating-point technique for extending the available precision. Mathematisch Centrum MR 118/70 (1970). MR 0299007
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