论文标题
分段恒定系数线性差分操作员在有限间隔和网络上对角线的fokas对角线化
Fokas diagonalization of piecewise constant coefficient linear differential operators on finite intervals and networks
论文作者
论文摘要
我们描述了具有任意线性边界条件的线性两点恒定系数差分算子的对角化的新形式。尽管对角度化的意义要比通常用于解决初始边界价值问题（IBVP）的意义较弱，但我们表明，解决该空间部分的IBVP足以由此类操作员描述。我们认为所描述的方法可以被视为在有限间隔上线性进化方程的FOKAS变换方法的重新实现。结果扩展到多点和接口操作员，包括在有限间隔网络上定义的运算符，其中差分运算符的系数可能在子间隔间之间有所不同，并且可以施加任意接口和边界条件。因此，包括具有分段恒定系数的差分运算符。均匀和不均匀的问题均已解决。
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.
