Numerical methods for ordinary different[ e-boek]

Numerical Methods for Ordinary Differential EquationsIn 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