Abstract:
more general linear iterative scheme solves non-linear equations arising in the
implementation of implicit Runge-Kutta methods proposed by Cooper and Butcher
is of the form
where B and S are real non-singular matrices and L is strictly lower triangular
matrix of order s, and is a real constant. They showed that successive over
relaxation technique applied to improve the convergence rate of this scheme. Later,
convergence result of this scheme established by proving some theoretical results
suitable for stiff problems. This article examines stability properties of this linear
iterative scheme with the alternate approximation
It is better to use because it requires less evaluation of f and is more accurate for
stiff problem. For a fixed starting value 0 Y
