Multistep Interval Methods of Nyström and Milne-Simpson Types

The paper is dealt with two kinds of multistep intervals methods which can be used to solve the initial value problem in the form of intervals containing all possible numerical errors. The interval methods of Nystrom type are explicit, while the methods of Milne- Simpson are implicit. It appears that we can get two families of interval methods of the second kind. For both kinds of interval methods numerical examples are presented and compared with other interval multistep method considered in previous papers of the author.

[1]  N. G. Parke,et al.  Ordinary Differential Equations. , 1958 .

[2]  P. Hartman.  Ordinary Differential Equations , 1965 .

[3]  Andrzej Marciniak.  Numerical Solutions of the N-Body Problem , 1985 .

[4]  J. Butcher.  The Numerical Analysis of Ordinary Di erential Equa-tions , 1986 .

[5]  J. Butcher.  The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods , 1987 .

[6]  Leslie Greengard,et al.  The numerical solution of the N-body problem , 1990 .

[7]  Andrzej Marciniak,et al.  ONE- AND TWO-STAGE IMPLICIT INTERVAL METHODS OF RUNGE-KUTTA TYPE , 1999 .

[8]  Andrzej Marciniak,et al.  THREE- AND FOUR-STAGE IMPLICIT INTERVAL METHODS OF RUNGE-KUTTA TYPE , 2000 .

[9]  Andrzej Marciniak,et al.  Implicit interval multistep methods for solving the initial value problem , 2002 .

[10]  Andrzej Marciniak,et al.  On explicit interval methods of Adams - Bashforth type , 2002 .

[11]  Andrzej Marciniak,et al.  Implicit Interval Methods for Solving the Initial Value Problem , 2004, Numerical Algorithms.

[12]  Andrzej Marciniak,et al.  ON REPRESENTATIONS OF COEFFICIENTS IN IMPLICIT INTERVAL METHODS OF RUNGE-KUTTA TYPE , 2004 .

[13]  Andrzej Marciniak,et al.  On Two Families of Implicit Interval Methods of Adams-Moulton Type , 2006 .

[14]  Andrzej Marciniak,et al.  On multistep interval methods for solving the initial value problem , 2007 .

[15]  Andrzej Marciniak,et al.  A Survey of Interval Runge-Kutta and Multistep Methods for Solving the Initial Value Problem , 2007, PPAM.