Inexact Newton method as a tool for solving differential-algebraic systems

The inexact Newton method is commonly known from its ability to solve large-scale systems of nonlinear equations. In the paper the classical inexact Newton method is presented as a tool for solving differential-algebraic equations (dae) in fully-implicit form F(ẏ, y, t) = 0. The appropriate statement of dae using the backward Euler method makes the possiblity to see the differential-algebraic system as a large-scale system of nonlinear equations. Because a choice of the forcing terms in the inexact Newton method significantly affects the convergence of the algorithm, in the paper new variants of the inexact Newton method were presented and tested. The simulations were executed in Matlab environment using Wroclaw Centre for Networking and Supercomputing.