Abstract:

       We construct the differentiation matrices of an unknown function regarding temporal and spatial variables for the given computational nodes in temporal and spatial fields with the approaximation of barycentric rational interpolation to the function. We initially acquire discrete algebraic equations of a wave equation and its definite conditions by inserting barycentric rational interpolation of an unknown function into the governing equation of the wave equation. We then denote the discrete algebraic equations as a concise matrix with the notation of differentiation matrices. We eventually obtain the displacements of the wave equation on the nodes by replacement method and applying boundary and initial conditions. Numerical examples demonstrate that the approach has such advantages as simple computation, easy programming and high precision.

Key words: wave motion problems, barycentric rational interpolation, differentiation matrix, collocation method