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Novel exact solutions for PDEs with mixed boundary conditions

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  • Mark Craddock
  • Martino Grasselli
  • Andrea Mazzoran

Abstract

We develop methods for the solution of inhomogeneous Robin type boundary value problems (BVPs) that arise for certain linear parabolic Partial Differential Equations (PDEs) on a half line, as well as a second order generalisation. We are able to obtain non-standard solutions to equations arising in a range of areas, including mathematical finance, stochastic analysis, hyperbolic geometry and mathematical physics. Our approach uses the odd and even Hilbert transforms. The solutions we obtain and the method itself seem to be new.

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  • Mark Craddock & Martino Grasselli & Andrea Mazzoran, 2023. "Novel exact solutions for PDEs with mixed boundary conditions," Papers 2311.12177, arXiv.org.
    • Handle: RePEc:arx:papers:2311.12177
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    File URL: http://arxiv.org/pdf/2311.12177
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    1. Craddock, Mark & Grasselli, Martino, 2020. "Lie symmetry methods for local volatility models," Stochastic Processes and their Applications, Elsevier, vol. 130(6), pages 3802-3841.
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