Abstract
We present a method to enclose fundamental solutions of linear ordinary differential equations, especially for a one dimensional Schrödinger equation which has a periodic potential. Our method is based on Floquet theory and Nakao’s verification method for nonlinear equations. We show how to enclose fundamental solutions together with characteristic exponents and give a numerical example.
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© 2008 Birkhäuser Verlag Basel/Switzerland
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Nagatou, K. (2008). Validated Computations for Fundamental Solutions of Linear Ordinary Differential Equations. In: Bandle, C., Losonczi, L., Gilányi, A., Páles, Z., Plum, M. (eds) Inequalities and Applications. International Series of Numerical Mathematics, vol 157. Birkhäuser, Basel. https://doi.org/10.1007/978-3-7643-8773-0_5
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DOI: https://doi.org/10.1007/978-3-7643-8773-0_5
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