Abstract
The relationship between the accuracy and stability of a semidiscretised finite difference scheme for solving the advection equation, ut = ux, is posed as an investigation into rational approximations to the logarithmic function. The geometric properties of such approximations are studied using the theory of order stars. In consequence we prove that the accuracy order p of the given stable scheme
is bounded by min{r+s+R+S, 2(r+R+1), 2(s+S)}. We also demonstrate that particular Padé approximations to ZLlnz are normal. Furthermore, using Padé theory we find stable methods attaining the bound on accuracy for various choices of r,s,R and S.
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5. References
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© 1984 Springer-Verlag
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Williamson, R.A. (1984). Pade approximations in the numerical solution of hyperbolic differential equations. In: Werner, H., Bünger, H.J. (eds) Padé Approximation and its Applications Bad Honnef 1983. Lecture Notes in Mathematics, vol 1071. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099623
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DOI: https://doi.org/10.1007/BFb0099623
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