A class of nonlinear multistep A-stable numerical methods for solving stiff differential equations

AbstractA family of nonlinear multistep (NLMS) methods is formulated to be A-stable in the sense of Dahlquist. These methods are a generalization of linear multistep methods and are particularly effective for solving differential equations whose solutions are asymptotically stable. NLMS methods have been applied to several ‘stiff’ differential equations whose solutions are illustrated. An analysis of step size choice is given