The numerical solution of differential-algebraic equations by least squares approximation

In this thesis, a method was presented to solve for systems of differential-algebraic equations arising in sciences and engineering. Firstly, differential-algebraic equation system was transformed to power series until arbitrary order, and then the system was solved numerically by using least squares approximation method. To illustrate this method, three different problems have been investigated. The numerical solutions of problems were compared with the their exact solutions and in maple programming the method has been programmed. Keywords: Differential-algebraic equations, power series, least squares approximations, index, arbitrary order.