ON ACCELERATING THE CONVERGENCE OF NONLINEAR ITERATIVE ALGORITHMS

The underlying theory of vector sequence extrapolation methods for lin ear and nonlinear problems is examined. It is shown that nonlinearity limits savings in total number of iterations to 50% for strongly nonli near problems when linear-based extrapolation methods are used. In sup port of this conclusion, convergence behaviors of solutions of Burgers ' equation and an interacting boundary layer problem are examined. Sup porting evidence from the work of previous researchers is also present ed. A possible means of circumventing this limitation by including non linear terms in the extrapolation is suggested. Results of this method for a scalar model problem and a solution to Burgers equation are giv en, showing that the 50% limitation can be circumvented. (C) 1994 Acad emic Press, Inc