Exponential Fitting

ISBN-13: 9781402020995 / Angielski / Twarda / 2004 / 308 str.

Guido Vanden Berghe; Liviu Gr Ixaru; Guido Vanden Berghe

Opis

Exponential Fitting is a procedure for an efficient numerical approach of functions consisting of weighted sums of exponential, trigonometric or hyperbolic functions with slowly varying weight functions. This book is the first one devoted to this subject. Operations on the functions described above like numerical differentiation, quadrature, interpolation or solving ordinary differential equations whose solution is of this type, are of real interest nowadays in many phenomena as oscillations, vibrations, rotations, or wave propagation.
The authors studied the field for many years and contributed to it. Since the total number of papers accumulated so far in this field exceeds 200 and the fact that these papers are spread over journals with various profiles (such as applied mathematics, computer science, computational physics and chemistry) it was time to compact and to systematically present this vast material.
In this book, a series of aspects is covered, ranging from the theory of the procedure up to direct applications and sometimes including ready to use programs. The book can also be used as a textbook for graduate students.

Recenzje

From the reviews:

"This book concerns exponential fitting in various areas of numerical analysis. It surveys recent research work in these areas with particular emphasis on the solution of initial value problems for ordinary differential equations. It will be of interest to researchers in application areas ... but more particularly to those investigating and extending algorithms for exponential fitting. ... FORTRAN95 code for most of the formulae is given in the text ... to make it easy to try out the formulae." (Kenneth Wright, Mathematical Reviews, Issue 2006 f)

Spis treści

Preface. Acknowledgements. 1: Introduction. 2: Mathematical Properties. 1. A reference differential equation. 2. A regularization procedure. 3. An outline of the exponential fitting procedure. 4. The theory of the exponential fitting approach. 3: Constructions of EF Formulae for Functions with Oscillatory or Hyperbolic Variation. 1. The Schrödinger equation. 2. Functions etas(Z), s = -1, 0, 1, 2,.... 3. A six-step flow chart. 4: Numerical Differentiation Quadrature and Interpolation. 1. Numerical differentiation. 2. Quadrature. 3. Interpolation. 5: Linear Multistep Solvers for Ordinary Differential Equations. 1. First order equations. 2. Second order equations. 6: Runge-Kutta Solvers for Ordinary Differential Equations. 1.Formalism and construction scheme for classical Runge-Kutta methods. 2. Exponential-fitted explicit methods. 3. Exponential-fitted implicit methods. 4. Some related research: Runge-Kutta-Nyström methods. CD contents. Topic Index.