On Solvability and Waveform Relaxation Methods for Linear Variable-coefficient Differential-algebraic Equations

This paper is concerned with the solvability and waveform relaxation methods of linear variable-coefficient differential-algebraic equations (DAEs). Most of the previous works have been focused on linear variable-coefficient DAEs with smooth coefficients and data, yet no results related to the convergence rate of the corresponding waveform relaxation methods has been obtained. In this paper, we develope the solvability theory for the linear variable-coefficient DAEs on Legesgue square-integrable function space in both traditional and least squares senses, and determine the convergence rate of the waveform relaxation methods for solving linear variable-coefficient DAEs.