Nonlinear Multistep Methods for Solving Initial Value Problems in Ordinary Differential Equations.

摘要

The report develops a family of Nonlinear Multistep (NLMS) numerical methods which solve initial value problems for systems of first-order differential equations. These methods are demonstrated to be a generalization of Linear Multistep (LMS) methods and are formulated to be particularly effective for equations whose solutions are asymptotically stable. The formal theory of NLMS methods with regard to stability,consistency,and convergence is fully developed and proved. NLMS methods are strongly stable and accommodate A-stability in the sense of Dahlquist. Extensive numerical test results produced by NLMS methods show important advantages over Adams'and Gear's methods and Ehle's test results. (Author)