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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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