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A Unified Analytical Approach to Fixed and Moving Boundary Problems for the Heat Equation

Author

Listed:
  • Marianito R. Rodrigo

    (School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW 2522, Australia)

  • Ngamta Thamwattana

    (School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, NSW 2308, Australia)

Abstract

Fixed and moving boundary problems for the one-dimensional heat equation are considered. A unified approach to solving such problems is proposed by embedding a given initial-boundary value problem into an appropriate initial value problem on the real line with arbitrary but given functions, whose solution is known. These arbitrary functions are determined by imposing that the solution of the initial value problem satisfies the given boundary conditions. Exact analytical solutions of some moving boundary problems that have not been previously obtained are provided. Moreover, examples of fixed boundary problems over semi-infinite and bounded intervals are given, thus providing an alternative approach to the usual methods of solution.

Suggested Citation

  • Marianito R. Rodrigo & Ngamta Thamwattana, 2021. "A Unified Analytical Approach to Fixed and Moving Boundary Problems for the Heat Equation," Mathematics, MDPI, vol. 9(7), pages 1-19, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:7:p:749-:d:527483
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    References listed on IDEAS

    as
    1. S. L. Mitchell & T. G. Myers, 2012. "Application of Heat Balance Integral Methods to One-Dimensional Phase Change Problems," International Journal of Differential Equations, Hindawi, vol. 2012, pages 1-22, April.
    2. Marianito R. Rodrigo, 2020. "Pricing of Barrier Options on Underlying Assets with Jump-Diffusion Dynamics: A Mellin Transform Approach," Mathematics, MDPI, vol. 8(8), pages 1-20, August.
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