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Numerical Solution of 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

We use a continuously differentiable representation of the numerical solution in order to define a residual, also known as a defect or deviation. This allows the use of backward error analysis on the numerical solution of initial-value problems (IVP) for ordinary differential equations. Of course, this means that we should also examine the conditioning or sensitivity of an IVP. We use the Matlab ODE Suite as an example of high-quality software. We pay some attention to chaotic problems, stiff problems, and singular problems. ⊲

Suggested Citation

  • Robert M. Corless & Nicolas Fillion, 2013. "Numerical Solution of ODEs," Springer Books, in: A Graduate Introduction to Numerical Methods, edition 127, chapter 0, pages 509-583, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-8453-0_12
    DOI: 10.1007/978-1-4614-8453-0_12
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