General method to solve the heat equation

ByoungSeon Choi, Daun Jeong and M.Y. Choi

Physica A: Statistical Mechanics and its Applications, 2016, vol. 444, issue C, 530-537

Abstract: General solutions of the heat equation are presented in terms of the Koopman–Darmois family of exponential functions, which include both the separable solution and the fundamental solution. In particular, we derive a new closed-form solution, which may not be obtained via the separation of variables or via an integral transform. It is demonstrated that the new solution describes the time evolution of the distribution of random walkers under an absorbing boundary.

Keywords: Heat equation; Diffusion equation; Random walk; Koopman–Darmois exponential function (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:444:y:2016:i:c:p:530-537

DOI: 10.1016/j.physa.2015.10.044

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