Abstract
We are concerned with a general class of finite difference schemes for −x″= f(t,x) under Dirichlet conditions. The schemes are built up of symmetric difference formulae. We prove computable upper bounds for the step width h such that the resulting scheme satisfies a stability inequality. This yields unique solvability of the scheme as well as the applicability of certain numerical methods to solve the system. We conclude with a discussion of the order of convergence of these schemes and apply our results to four particular cases of order 2,4 and 6.
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Bohl, E. (1976). Zur Anwendung von Differenzenschemen mit Symmetrischen Formeln bei Randwertaufgaben. In: Albrecht, J., Collatz, L. (eds) Moderne Methoden der Numerischen Mathematik. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D’Analyse Numérique, vol 32. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5501-3_3
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DOI: https://doi.org/10.1007/978-3-0348-5501-3_3
Publisher Name: Birkhäuser, Basel
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