Abstract
We consider a noncharacteristic initial value problem for a hyperbolic differential equation
a(x, y, µ )u xx + b(x,y, µ )ux y + c(x, y, µ ) µ yy = f (x, y, µ, µ x , µ y ).
The paper presents1 a method which yields pointwise enclosures of the domain of determinacy\( \widehat M \)(depending implicitly on µ) and of the corresponding solution µ(x,y), (x, y) ∈\( \widehat M \)The method has been implemented on a computer using machine interval arithmetic.
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References
E.W. Kaucher and W.L. Miranker, Self-Validating Numerics for Function Space Problems, Academic Press, New York, 1984.
L.B. Rall, Automatic Differentiation: Techniques and Applications, Springer-Verlag, Berlin, Heidelberg, New York, 1981.
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Koeber, M. (1999). Inclusion of Solutions of Cauchy Problems for Quasilinear Hyperbolic Equations. In: Jeltsch, R., Fey, M. (eds) Hyperbolic Problems: Theory, Numerics, Applications. International Series of Numerical Mathematics, vol 130. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8724-3_8
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DOI: https://doi.org/10.1007/978-3-0348-8724-3_8
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9744-0
Online ISBN: 978-3-0348-8724-3
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