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Journal article
Fokas Diagonalization of Piecewise Constant Coefficient Linear Differential Operators on Finite Intervals and Networks
Acta applicandae mathematicae, v 177(1), 2
01 Feb 2022
Abstract
We describe a new form of diagonalization for linear two point constant coefficient differential operators with arbitrary linear boundary conditions. Although the diagonalization is in a weaker sense than that usually employed to solve initial boundary value problems (IBVP), we show that it is sufficient to solve IBVP whose spatial parts are described by such operators. We argue that the method described may be viewed as a reimplementation of the Fokas transform method for linear evolution equations on the finite interval. The results are extended to multipoint and interface operators, including operators defined on networks of finite intervals, in which the coefficients of the differential operator may vary between subintervals, and arbitrary interface and boundary conditions may be imposed; differential operators with piecewise constant coefficients are thus included. Both homogeneous and inhomogeneous problems are solved.
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Details
- Title
- Fokas Diagonalization of Piecewise Constant Coefficient Linear Differential Operators on Finite Intervals and Networks
- Creators
- Sultan Aitzhan - Drexel UniversitySambhav Bhandari - Yale-NUS CollegeDavid A. Smith - Yale-NUS College
- Publication Details
- Acta applicandae mathematicae, v 177(1), 2
- Publisher
- Springer Nature
- Number of pages
- 69
- Grant note
- Yale-NUS College summer research programme 2019 Yale-NUS College summer research programme 2020 IG18-PRB102 / Yale-NUS College project EP/R014604/1 / EPSRC; UK Research & Innovation (UKRI); Engineering & Physical Sciences Research Council (EPSRC)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000737978400001
- Scopus ID
- 2-s2.0-85122205933
- Other Identifier
- 991021861192804721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics, Applied