Deriving general solutions of the heat-transfer and the Fokker–Planck boundary-value problems through modified separation methods

Daun Jeong and ByoungSeon Choi

Physica A: Statistical Mechanics and its Applications, 2020, vol. 556, issue C

Abstract: We present modified separation methods to solve the heat equation, which provide the general solutions in terms of a non-separable basis. This basis not only covers the set of the Hermite polynomials but also a more general set of confluent hypergeometric functions, which are known from the similarity solution of the heat equation. Modifying the closed form solutions of the heat equation with an exponential weight, we derive corresponding partial differential equations, which include simple cases of the Fokker–Planck equation. Their closed form solutions are thus provided.

Keywords: Partial differential equation; Diffusion; Heat transfer equation; Separation method; Fokker–Planck equation; Hermite polynomial; Confluent hypergeometric function (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:556:y:2020:i:c:s0378437120304301

DOI: 10.1016/j.physa.2020.124831

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