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Keywords:
Picard method; Seidel method; system of differential algebraic equations; convergence; successive approximations; differential algebraic equations; comparison method; Picard iterations
Picard method; Seidel method; system of differential algebraic equations; convergence; successive approximations; differential algebraic equations; comparison method; Picard iterations
Summary:
In the paper the comparison method is used to prove the convergence of the Picard iterations, the Seidel iterations, as well as some modifications of these methods applied to approximate solution of systems of differential algebraic equations. The both linear and nonlinear comparison equations are emloyed.
References:
[1] E. Bohl: Monotonie: Lösbarkeit und Numerik bei Operatoren-gleichungen. Springer Verlag, Berlin, 1974. MR 0636414
[2] I. Bremer K.R. Schneider: A remark on solving large systems of equations in function spaces. Aplikace Matematiky 35(1990), 494-498. MR 1089930
[3] L. Kantorovich: The method of successive approximations for functional equations. Acta Math. 71 (1939), 63-97. DOI 10.1007/BF02547750 | MR 0000095
[4] M. Kwapisz: On the approximate solutions of an abstract equation. Ann. Polon. Math. 19 (1967), 47-60. DOI 10.4064/ap-19-1-47-60 | MR 0210314 | Zbl 0149.36403
[5] M. Kwapisz: On the convergence of approximate iterations for an abstract equation. Ann. Polon. Math. 22(1969), 73-87. DOI 10.4064/ap-22-1-73-87 | MR 0258274 | Zbl 0184.37802
[6] M. Kwapisz: A comparison theorem on the existence and uniqueness of the solution of an integral-functional equation. VII Internationale Konferenz über nichtlineare Schwingungen, Band 1,1, Abhandlungen der AdW, Akademie-Verlag, Berlin, 1977, pp. 481-487. MR 0513188 | Zbl 0368.45009
[7] M. Kwapisz: Some remarks on abstract form of iterative methods in functional equation theory. Commentationes Mathematicae 24 (1984), 281-294. MR 0766465 | Zbl 0579.47064
[8] M. Kwapisz: Some remarks on nonlinear A-contractions. Analele Sţiintifice Ale Universitătii "Al. I. Cuza" - Iasi, 32, s. I a, Mathematică 2 (1986), 17-22. MR 0893678 | Zbl 0652.47037
[9] J. M. Ortega W. C. Rheinboldt: Iterative solutions of nonlinear equations in several variables. Academic Press, New York, 1970. MR 0273810
[10] T. Wazewski: Sur un precédé de prouver la convergence des approximations successives sans utilisation des séries de comparison. Bull. Acad. Sci., sér. sci. math. astr. et phys. 8, 1 (1960), 45-52. MR 0126109
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