Ordinary Differential Equations

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


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,
$$y' = f\left( {x,y} \right);$$
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
$$ y\left( {{x_o}} \right) = {y_o} $$


Ordinary Differential Equation Extrapolation Method Multistep Method Midpoint Rule Linear Multistep Method 
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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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