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Some initial-boundary value problems

In: Application of Holomorphic Functions in Two and Higher Dimensions

Author

Listed:
  • Klaus Gürlebeck

    (Bauhaus-Universität Weimar)

  • Klaus Habetha

    (RWTH Aachen)

  • Wolfgang Sprößig

    (TU Bergakademie Freiberg)

Abstract

In this chapter we will study initial-boundary value problems and their treatment by methods of quaternionic analysis in combination with classical analytic numerical techniques. We start with a brief discussion of strategies for the treatment of time-dependent parabolic problems. Three methods should be considered here: the horizontal method of lines, better known as the Rothe method, the Witt basis approach, and the harmonic extension method. The studies of parabolic problems go back to the pioneering work of Jean Joseph Fourier on heat propagation in an ideal bar in the first two decades of the 19th century.

Suggested Citation

  • Klaus Gürlebeck & Klaus Habetha & Wolfgang Sprößig, 2016. "Some initial-boundary value problems," Springer Books, in: Application of Holomorphic Functions in Two and Higher Dimensions, chapter 0, pages 265-301, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-0964-1_8
    DOI: 10.1007/978-3-0348-0964-1_8
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