On using Newton-type iterative methods for solving systems of differential-algebraic equations of index 1
Kulikov, Gennady Yu
Computational Mathematics and Mathematical Physics, 41(8) (2001), 1122-1131
The applicability of Newton-type iterative methods to the solution of systems of differential-algebraic equations of index 1 is examined. A new combined numerical method based on the Euler method and general Newton iterations is designed. The convergence of the method is proved, and an error estimate for the numerical solution is obtained. Some observations on the practical value of the new method are provided, and directions for future research on this subject are indicated.