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math.SP2020
Fokas diagonalization of piecewise constant coefficient linear differential operators on finite intervals and networks
Sultan Aitzhan, Sambhav Bhandari, David Andrew Smith
We describe a new form of diagonalization for linear two point constant coefficient differential operators with arbitrary linear boundary conditions. Although the diagonalization i…
math.SP2014
The unified transform method for linear initial-boundary value problems: a spectral interpretation
David A. Smith
It is known that the unified transform method may be used to solve any well-posed initial-boundary value problem for a linear constant-coefficient evolution equation on the finite…
math.SP2013★ 2 cited
Evolution PDEs and augmented eigenfunctions. Finite interval
David Andrew Smith, Athanassios S. Fokas
The so-called unified method expresses the solution of an initial-boundary value problem (IBVP) for an evolution PDE in the finite interval in terms of an integral in the complex F…