2020/12/10 by Sultan Aitzhan, Aitzhan, Sultan, Sambhav Bhandari +3
Mathematics · Physics and Astronomy · #35G16 #35P10 (primary). 35C15 #47A70 (secondary) #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Waves and Solitons #Numerical methods for differential equations #Spectral Theory (math.SP)
paper · pdf · doi:10.48550/arxiv.2012.05638
openalex publication_date 2020/12/10 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
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.