Stability and Convergence of Variable Order Multistep Methods

Stability and B-convergence properties of multistep Runge-Kutta methods

This paper continues earlier work by the same author concerning the stability and B-convergence properties of multistep Runge-Kutta methods for the numerical solution of nonlinear stiff initial-value problems in a Hilbert space. A series of sufficient conditions and necessary conditions for a multistep Runge-Kutta method to be algebraically stable, diagonally stable, Bor optimally B-convergent ...

Multistep Methods for Coupled Second Order Integro-differential Equations: Stability, Convergence and Error Bounds

In this paper multistep methods for systems of coupled second order Volterra integrodifferential equations are proposed. Stability and convergence properties are studied and an error bound for the discretization error is given.

Stability of implicit - explicit linear multistep methods

In many applications, large systems of ordinary di erential equations (ODEs) have to be solved numerically that have both sti and nonsti parts. A popular approach in such cases is to integrate the sti parts implicitly and the nonsti parts explicitly. In this paper we study a class of implicit-explicit (IMEX) linear multistep methods intended for such applications. The paper focuses on the linea...

ON ACCURACY AND UNCONDITIONAL STABILITY OF LINEAR MULTISTEP METHODS FOR SECOND ORDER DIFFERENTIAL EQUATIONS bY

An Extended Multistep Shanks Transformation and Convergence Acceleration Algorithm with Their Convergence and Stability Analysis

The molecule solution of an extended discrete Lotka-Volterra equation is constructed, from which a new sequence transformation is proposed. A convergence acceleration algorithm for implementing this sequence transformation is found. It is proved that our new sequence transformation accelerates some kinds of linear sequences and factorial sequences with good numerical stability. Some numerical e...