Numerical methods for ordinary differential equations

Samenvatting

Numerical Methods for Ordinary Differential EquationsA big advantage of numerical mathematics is that a numerical solution can beobtained for problems, where an analytical solution does not exist. An additionaladvantage is, that a numerical method only uses evaluation of standard functions andthe operations: addition, subtraction, multiplication and division. Because these arejust the operations a computer can perform, numerical mathematics and computersform a perfect combination.An analytical method gives the solution as a mathematical formula, which is anadvantage. From this we can gain insight in the behavior and the properties of thesolution, and with a numerical solution (that gives the function as a table) this is notthe case. On the other hand some form of visualization may ... be used to gain insightin the behavior of the solution. To draw a graph of a function with a numerical methodis usually a more useful tool than to evaluate the analytical solution at a great numberof points.In this book we discuss several numerical methods for solving ordinary differentialequations. We emphasize those aspects that play an important role in practicalproblems. In this introductory text we confine ourselves to ordinary differentialequations with the exception of the last chapter in which we discuss the heatequation, a parabolic partial differential equation. The techniques discussed inthe introductory chapters, for e.g. interpolation, numerical quadrature and the solutionof 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 numericalspects are concerned.Contents: Preface | 1. Introduction | 2. Interpolation | 3. Numerical differentiation |4. Nonlinear equations | 5. Numerical quadrature | 6. Numerical time integration ofinitial value problems | 7. The finite difference method for boundary value problems |8. The instationary equation | Literature | IndexPublished by VSSDURL about this book: http://www.vssd.nl/hlf/a026.htm