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.
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© 2016 Springer International Publishing, Switzerland
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Gürlebeck, K., Habetha, K., Sprößig, W. (2016). Some initial-boundary value problems. In: Application of Holomorphic Functions in Two and Higher Dimensions. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0964-1_8
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DOI: https://doi.org/10.1007/978-3-0348-0964-1_8
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Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-0962-7
Online ISBN: 978-3-0348-0964-1
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