Exponential Fitting

Authors: Liviu Gr. Ixaru, Guido Vanden Berghe



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.

Table of contents

Front Matter
Pages i-xiv

Introduction
Pages 1-10

Mathematical Properties
Pages 11-52

Construction of EF Formulae for Functions with Oscillatory or Hyperbolic Variation
Pages 53-75

Numerical Differentiation, Quadrature and Interpolation
Pages 77-144

Linear Multistep Solvers for Ordinary Differential Equations
Pages 145-222

Runge-Kutta Solvers for Ordinary Differential Equations
Pages 223-304

Back Matter
Pages 305-308