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Numerical Methods for ODEs

In: A Graduate Introduction to Numerical Methods

Author

Listed:
  • Robert M. Corless

    (University of Western Ontario, Applied Mathematics)

  • Nicolas Fillion

    (University of Western Ontario, Applied Mathematics)

Abstract

This chapter gives a very brief survey of Runge–Kutta methods, including continuous explicit Runge–Kutta methods. We also discuss multistep methods and the Taylor series method (i.e., analytic continuation). We talk about implicit methods for stiff problems and backward error by the method of modified equations. We mention some of the several flavors of stability of a numerical method for solving IVP that are sometimes useful. We talk about interpolants and the residual and compare the residual with local error per unit step. We sketch methods for adaptive step-size control. ⊲

Suggested Citation

  • Robert M. Corless & Nicolas Fillion, 2013. "Numerical Methods for ODEs," Springer Books, in: A Graduate Introduction to Numerical Methods, edition 127, chapter 0, pages 585-693, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-8453-0_13
    DOI: 10.1007/978-1-4614-8453-0_13
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