Numerical Tau Method for Solving DAEs in Banach Spaces with Schauder Bases

摘要

Differential algebraic equations (DAEs) appear in many fields of physics and have a wide range of applications in various branches of science and engineering. Finding reliable methods to solve DAEs has been the subject of many investigations in recent years. In this paper, we present a numerical method for approximating the solution of a DAE. We formulate a general problem in a Banach space making use of a Schauder basis and the Tau method to approximate the load function and the solution of the differential problem. Finally, we offer a numerical example. This technique provides converges to the exact solution of the problem. The scheme is tested for some high-index DAEs and the results demonstrate that the method is very straightforward and can be considered as a powerful mathematical tool.