A class of variable mesh multistep methods for solving simultaneous nonlinear equations

In a recent paper P.T. Boggs has demonstrated the use of fixed mesh A-stable integration techniques in solving simultaneous nonlinear equations. This paper treats a class of variable mesh multistep methods. The affect of slap size chinge on convergence is examined closely. It is shown that with suitable control on step size change a variable mesh linear multistep method is convergent if the underlying fixed mesh method satisfy certain conditions. Implicit and explicit Adams methods of order less than five and three satisfy these requirements readily. Finally the effectiveness of the proposed method: are demonstrated in numerical tostings using a practical algorithm for automatic step size control.Technical report DCS-TR-2