Exponential multistep methods of Adams-type

Exponential multistep methods of Adams-type

The paper is concerned with the construction, implementation and numerical analysis of exponential multistep methods. These methods are related to explicit Adams methods but, in contrast to the latter, make direct use of the exponential and related matrix functions of a (possibly rough) linearization of the vector field. This feature enables them to integrate stiff problems explicitly in time. ...

Experiments in stepsize control for Adams linear multistep methods

The Multistep Methods of Mart N and Ferr Andiz as Modied Adams Methods

The SMF methods of Mart n and Ferr andiz [SIAM J. Numer. Anal. 34 (1997) 359-375], for di erential equations of second order, are shown to be equivalent to modi ed Adams methods. This leads to new formulae for the coe cients of those methods, generating functions analogous to those of the Adams methods for equations of rst order, and simpler, more instructive, expressions for the local truncati...

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...

Exponential Rosenbrock-Type Methods

We introduce a new class of exponential integrators for the numerical integration of large-scale systems of stiff differential equations. These so-called Rosenbrock-type methods linearize the flow in each time step and make use of the matrix exponential and related functions of the Jacobian. In contrast to standard integrators, the methods are fully explicit and do not require the numerical sol...