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Padé extension of Bergman-series solutions to nonlinear boundary-value problems in heat conduction

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Summary

Bergman-type series solutions involving iterated complementary error integrals are constructed for nonlinear boundary-value problems associated with heat conduction in a region bounded internally by a cylindrical or spherical surface. In particular, a small-time solution is developed when the nonlinear boundary condition is of the Stefan-Boltzmann type. This solution is extended via Padé approximants.

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Author notes

  1. C. Rogers

    Present address: Department of Applied Mathematics, University of Waterloo, N2L 3GI, Waterloo, Ontario, Canada

Authors and Affiliations

  1. School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia, USA

    C. Rogers

  2. Department of Mathematics and Statistics, University of New Brunswick, Fredericton, Canada

    D. W. Barclay

  3. Department of Applied Mathematics, University of Adelaide, Adelaide, Australia

    D. L. Clements

Authors
  1. C. Rogers
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  2. D. W. Barclay
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  3. D. L. Clements
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Rogers, C., Barclay, D.W. & Clements, D.L. Padé extension of Bergman-series solutions to nonlinear boundary-value problems in heat conduction. J Eng Math 20, 145–161 (1986). https://doi.org/10.1007/BF00042773

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  • DOI: https://doi.org/10.1007/BF00042773

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