Fokas Diagonalization of Piecewise Constant Coefficient Linear Differential Operators on Finite Intervals and Networks

@article{Aitzhan2020FokasDO,
  title={Fokas Diagonalization of Piecewise Constant Coefficient Linear Differential Operators on Finite Intervals and Networks},
  author={Sultan Aitzhan and Sambhav Bhandari and David A. Smith},
  journal={Acta Applicandae Mathematicae},
  year={2020},
  volume={177},
  pages={1-69}
}
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… 

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