Exponential Fitting (Mathematics and Its Applications, 568)

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. Introduction -- Mathematical Properties -- Construction Of Ef Formulae For Functions With Oscillatory Or Hyperbolic Variation -- Numerical Differentiation, Quadrature And Interpolation -- Linear Multistep Solvers For Ordinary Differential Equations -- Runge-kutta Solvers For Ordinary Differential Equations. Edited By Liviu Gr. Ixaru And Guido Vanden Berghe. Includes Bibliographical References And Index.

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.

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