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Numerical Methods for Initial Value Problems

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A First Course in Ordinary Differential Equations

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Abstract

With this chapter, the numerical part of the book begins. Here, numerical methods for initial value problems of systems of first-order differential equations are studied. Starting with the concept of discretizing differential equations, the class of Runge-Kutta methods is introduced. The Butcher schemes of a variety of Runge-Kutta methods are given. Further topics are consistency, convergence, estimation of the local discretization error, step-size control, A-stability, and stiffness.

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Authors and Affiliations

  1. Institute of Applied Mathematics, Friedrich Schiller University, Jena, Germany

    Martin Hermann

  2. Department of Mathematics, Islamic Azad University Nour Branch, Nour, Iran

    Masoud Saravi

Authors
  1. Martin Hermann
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  2. Masoud Saravi
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Hermann, M., Saravi, M. (2014). Numerical Methods for Initial Value Problems. In: A First Course in Ordinary Differential Equations. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1835-7_7

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