Exponential Fitting (Hardcover, 2004)

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 Schrodinger 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-Nystrom methods. CD contents. Topic Index.