A Family of Compact Linear Multistep Methods With Thirdorder Accuracy for Solving Ordinary Differential Equations

Abstract

This work presents the results of the development of a one-parameter family of compact linear multistep methods of third order accuracy for solving the Cauchy problem for a first-order ordinary differential equation. A distinguishing feature of this method is that the elements of the vector of the sought variables are not predetermined before constructing the method. Conditions for zero-stable stability were obtained, and zones of A-stability were constructed for different values of the family parameter. It is shown that the stability areas of the family of methods proposed in the work are significantly larger than the stability areas of classical linear multistep methods. Practical recommendations for choosing a parameter are also given.