Stability of multistep methods for delay differential equations

Linear Multistep Methods for Impulsive Differential Equations

This paper deals with the convergence and stability of linear multistep methods for impulsive differential equations. Numerical experiments demonstrate that both the mid-point rule and twostep BDFmethod are of order p 0when applied to impulsive differential equations. An improved linear multistep method is proposed. Convergence and stability conditions of the improved methods are given in the p...

Stability of two classes of improved backward Euler methods for stochastic delay differential equations of neutral type

This paper examines stability analysis of two classes of improved backward Euler methods, namely split-step $(theta, lambda)$-backward Euler (SSBE) and semi-implicit $(theta,lambda)$-Euler (SIE) methods, for nonlinear neutral stochastic delay differential equations (NSDDEs). It is proved that the SSBE method with $theta, lambdain(0,1]$ can recover the exponential mean-square stability with some...

‎Multistep collocation method for nonlinear delay integral equations

‎The main purpose of this paper is to study the numerical solution of nonlinear Volterra integral equations with constant delays, based on the multistep collocation method. These methods for approximating the solution in each subinterval are obtained by fixed number of previous steps and fixed number of collocation points in current and next subintervals. Also, we analyze the convergence of the...

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

Exponential Fitting of Matricial Multistep Methods for Ordinary Differential Equations

We study a class of explicit or implicit multistep integration formulas for solving N X N systems of ordinary differential equations. The coefficients of these formulas are diagonal matrices of order N, depending on a diagonal matrix of parameters Q of the same order. By definition, the formulas considered here are exact with respect to y = Dy + 4>(x, y) provided Q — hD, h is the integration st...