Summary
We develop a method for splitting certain linear two-point boundary value problems of the fourth order into problems of the second order which can be solved successively. Both, the given differential equation and the boundary conditions, are involved in the splitting.
The method is constructive and can be realized numerically. The resulting discrete second order problems are solved by thereduction method [4], which is distinguished by its special numerical stability.
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Literatur
Fox, L.: The numerical solution of two-point boundary value problems in ordinary differential equations. London: Oxford Univ. Press 1957
Hartman, P.: Principal solutions of disconjugaten-th order linear differential equations. Amer. J. Math.91, 306–362 (1969)
Schröder, J.: Randwertaufgaben vierter Ordnung mit positiver Greenscher Funktion. Math. Z.90, 429–440 (1965)
Schröder, J., Trottenberg, U.: Reduktionsverfahren für Differenzengleichungen bei Randwertaufgaben I. Numer. Math.22, 37–68 (1973)
Trottenberg, U.: An elementary calculus for Green's functions associated with singular boundary value problems. In: Ordinary and Partial Differential Equations, Proceedings of the Conference held at Dundee in 1974; 434–438. Berlin-Heidelberg-New York: Springer 1974
Trottenberg, U.: Aufspaltungen linearer gewöhnlicher Differentialoperatoren und der zugehörigen Greenschen Funktionen. Manuscripta math.15, 289–308 (1975)
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Trottenberg, U. Lösung linearer gewöhnlicher Randwertaufgaben 4. Ordnung mit Hilfe von Aufspaltungen. Numer. Math. 25, 297–306 (1975). https://doi.org/10.1007/BF01399419
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DOI: https://doi.org/10.1007/BF01399419