Numerical Methods For Ordinary Different

Numerical Methods for Ordinary Differential Equations In this book we discuss several numerical methods for solving ordinary differential equations. We emphasize the aspects that play an important role in practical problems. We confine ourselves to ordinary differential equations with the exception of the last chapter in which we discuss the heat equation, a parabolic partial differential equation. The techniques discussed in the introductory chapters, for instance interpolation, numerical quadrature and the solution to nonlinear equations, may also be used outside the context of differential equations. They have been included to make the book self-contained as far as the numerical aspects are concerned. Contents: Preface - 1. Introduction - 2. Interpolation - 3. Numerical differentiation - 4.Nonlinear equations - 5. Numerical integration - 6. Numerical time integration of initial-value problems - 7. The finite-difference method for boundary-value problems - 8. The instationary heat equation- Literature - Index

Developments in numerical initial value ode methods were the focal topic of the meeting at L'Aquila which explord the connections between the classical background and new research areas. This title includes proceedings that address many of these topics in both research and survey papers. Developments in numerical initial value ode methods were the focal topic of the meeting at L'Aquila which explord the connections between the classical background and new research areas such as differental-algebraic equations, delay integral and integro-differential equations, stability properties, continuous extensions (interpolants for Runge-Kutta methods and their applications, effective stepsize control, parallel algorithms for small- and large-scale parallel architectures). The resulting proceedings address many of these topics in both research and survey papers.