Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Solving Ordinary Differential Equations

P-stable linear symmetric multistep methods for periodic initial-value problems

The data-based mechanistic (DBM) approach to modelling has developed as a stochastic, ‘top-down’ response to the problems associated with the deterministic, ‘bottom-up’ approach. As such, it can be compared with the deterministic, top-down modelling methods that have been attracting attention recently in the hydrological literature. Using catchment-scale rainfall–flow modelling as an example, this paper compares the inductive DBM approach with its hypothetico-deductive, deterministic alternative and shows how they can be used to identify and estimate low-order, nonlinear models of the rainfall–flow dynamics in the River Hodder catchment of northwest England based on a limited set of rainfall–flow data. Copyright © 2003 John Wiley & Sons, Ltd.

Top‐down and data‐based mechanistic modelling of rainfall–flow dynamics at the catchment scale

A finite-difference method for the numerical solution of the Schro¨dinger equation

For any n and l values, we present a simple exact analytical solution ofthe radial Schrodinger equation for the Kratzer potential within the framework of theasymptotic iteration method (AIM). The exact bound-state energy eigenvalues ( E nl ) andcorresponding eigenfunctions ( R nl ) are calculated for various values of n and l quantum numbers for CO, NO, O 2 , and I 2 diatomic molecules. © 2006 Wiley Periodicals, Inc.Int J Quantum Chem 107: 540–544, 2007 Key words: asymptotic iteration method (AIM); bound states; eigenvalues andeigenfunctions; Kratzer potential; analytical solution 1. Introduction T he analytical solution of the radial Schrodingerequation is of high importance in nonrelativis-tic quantum mechanics, since the wave functioncontains all the necessary information to describe aquantum system fully. There are only a few poten-tials for which the radial Schrodinger equation can Correspondence to: O. Bayrak; e-mail: obayrak@erciyes.edu.trContract grant sponsor: Scientiﬁc and Technical ResearchCouncil of Turkey (TUBITAK).˙Contract grant number: TBAG-2398.Contract grant sponsor: Erciyes University.Contract grant numbers: FBA-03-27; FBT-04-15; FBT-04-16.

Exact analytical solutions to the Kratzer potential by the asymptotic iteration method

An exponentially-fitted Runge-Kutta method for the numerical integration of initial-value problems with periodic or oscillating solutions

A four-step method with phase-lag of infinite order is developed for the numerical integration of second order initial-value problems. Extensive numerical testing indicates that this new method can be generally more accurate than other four-step methods.

T. E. Simos

Papers

An exponentially-fitted Runge-Kutta method for the numerical integration of initial-value problems with periodic or oscillating solutions

A finite-difference method for the numerical solution of the Schro¨dinger equation

A four-step phase-fitted method for the numerical integration of second order initial-value problems

An optimized Runge-Kutta method for the solution of orbital problems

On finite difference methods for the solution of the Schrödinger equation