An efficient implementation scheme of the simplified Newton iteration for block systems of nonlinear equations (Q5953945)

The author presents an implementation scheme of the simplified Newton's iteration for solving a system of nonlinear equations obtained when an implicit general linear method is applied in order to compute the solution of an initial value problem for a stiff system of ordinary differential equations of the form NEWLINE\[NEWLINEy'=f(y), \quad y(t_0)=y_0, \quad t_0 <t \leq T, \quad f:\Omega \subset \mathbb R^n \to \mathbb R^m,\;m \gg 0.NEWLINE\]NEWLINE NEWLINENEWLINENEWLINEUsing a real similarity transformation for an arbitrary nonsingular matrix, the given implementation scheme has good intrinsic parallelism and is suitable for solving large systems often arising in practical applications.