Dw. Black et Ap. Rothmayer, ON ACCELERATING THE CONVERGENCE OF NONLINEAR ITERATIVE ALGORITHMS, Journal of computational physics, 111(2), 1994, pp. 324-335
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