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Ordinary Differential Equations

  • J. Stoer
  • R. Bulirsch
Part of the Texts in Applied Mathematics book series (TAM, volume 12)

Abstract

Many problems in applied mathematics lead to ordinary differential equations. In the simplest case one seeks a differentiable function y = y(x) of one real variable x, whose derivative y’(x) is to satisfy an equation of the form y’(x) = f (x, y(x)), or more briefly,
$$y' = f\left( {x,y} \right);$$
(7.0.1)
one then speaks of an ordinary differential equation. In general there are infinitely many different functions y which are solutions of (7.0.1). Through additional requirements one can single out certain solutions from the set of all solutions. Thus, in an initial-value problem, one seeks a solution y of (7.0.1) which for given xo, y o satisfies an initial condition of the form
$$ y\left( {{x_o}} \right) = {y_o} $$
(7.0.2)

Keywords

Ordinary Differential Equation Extrapolation Method Multistep Method Midpoint Rule Linear Multistep Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • J. Stoer
    • 1
  • R. Bulirsch
    • 2
  1. 1.Institut für Angewandte MathematikUniversität WürzburgWürzburgGermany
  2. 2.Institut für MathematikTechnische UniversitätMünchenGermany

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