### Analysis of the accuracy and convergence of equation-free projection to a slow manifold

In [C.W. Gear, T.J. Kaper, I.G. Kevrekidis and A. Zagaris, (2005) 711–732], we developed a class of iterative algorithms within the context of equation-free methods to approximate low-dimensional, attracting, slow manifolds in systems of differential equations with multiple time scales. For user-specified values of a finite number of the observables, the th member of the class of algorithms ($m=0,1,...$) finds iteratively an approximation of the appropriate zero of the st time derivative of the remaining...