Exponential Fitting

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.

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)