STABILITY AND CONVERGENCE OF STEPSIZE-DEPENDENT LINEAR MULTISTEP METHODS FOR NONLINEAR DISSIPATIVE EVOLUTION EQUATIONS IN BANACH SPACE

Stability and global error bounds are studied for a class of stepsize-dependent linear multistep methods for nonlinear evolution equations governed by omega-dissipative vector fields in Banach space. To break through the order barrier p <= 1 of unconditionally contractive linear multistep methods for dissipative systems, strongly dissipative systems are introduced. By employing the error growth function of the methods, new contractivity and convergence results of stepsize-dependent linear multistep methods on infinite integration intervals are provided for strictly dissipative systems (omega < 0) and strongly dissipative systems. Some applications of the main results to several linear multistep methods, including the trapezoidal rule, are supplied. The theoretical results are also illustrated by a set of numerical experiments.