Numerical Solution of Ordinary Differential Equations

  • Alfio Quarteroni
  • Riccardo Sacco
  • Fausto Saleri
Part of the Texts in Applied Mathematics book series (TAM, volume 37)


In this chapter we deal with the numerical solutions of the Cauchy problem for ordinary differential equations (henceforth abbreviated by ODEs). After a brief review of basic notions about ODEs, we introduce the most widely used techniques for the numerical approximation of scalar equations. The concepts of consistency, convergence, zero-stability and absolute stability will be addressed. Then, we extend our analysis to systems of ODEs, with emphasis on stiff problems.


Absolute Stability Multistep Method Local Truncation Error Linear Multistep Method Root Condition 
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Copyright information

© Springer Science+Business Media New York 2007

Authors and Affiliations

  • Alfio Quarteroni
    • 1
  • Riccardo Sacco
    • 2
  • Fausto Saleri
    • 3
  1. 1.Department of MathematicsEcole Polytechnique, Fédérale de LausanneLausanneSwitzerland
  2. 2.Dipartimento di MatematicaPolitecnico di MilanoMilanItaly
  3. 3.Dipartimento di Matematica, “F. Enriques”Università degli Studi di MilanoMilanItaly

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