Abstract:
A modified Newton scheme is typically used to
solve large sets of non-linear equations arising in the implementation of implicit Runge-Kutta methods. As an alternative to
this scheme, iteration schemes, which sacrifice superlinear convergence for reduced linear algebra costs, have been proposed.
A more general linear iterative scheme of this type proposed by
Cooper and Butcher in 1983 for implicit Runge-Kutta methods,
and he has applied the successive over relaxation technique to
improve the convergence rate. In this paper, we establish the
convergence result of this scheme by proving some theoretical
results suitable for stiff problems. Also these convergence results
are verified by two and three stage Gauss method and Radue
IIA method.
