Analysis of generalized multistep Adam's methods by degenerate matrix method for ordinary differential equations

Abstract

Adam's methods in the multistep mode are considered by means of general schemes of the degenerate matrix method. The stability function for these methods is computed by the residue theory on the complex plane. Performance of uniformly and non‐uniformly distributed nodes in the standardized interval is compared.

Darbe nagrinejamas daugiažingsnis Adamso metodas. Jis formuluojamas kaip atskiras atvejis bendros išsigimstančiu matricu schemos. Naudojantis rezidiumu metodu ištirtas Adamso metodo stabilumas. Palygintos stabilumo sritys, kai diskretieji mazgai yra pasiskirste tolygiai ir netolygiai.