Solution of parabolic free boundary problems using transmuted heat polynomials

Igor V. Kravchenko; Vladislav V. Kravchenko; Sergii M. Torba

Solution of parabolic free boundary problems using transmuted heat polynomials

Analysis of PDEs 2017-07-21 v2 Mathematical Physics math.MP Numerical Analysis

Authors: Igor V. Kravchenko , Vladislav V. Kravchenko , Sergii M. Torba

Abstract

A numerical method for free boundary problems for the equation $u_{xx}-q(x)u=u_t$ is proposed. The method is based on recent results from transmutation operators theory allowing one to construct efficiently a complete system of solutions for this equation generalizing the system of heat polynomials. The corresponding implementation algorithm is presented.

Keywords

heat equation

Cite

@article{arxiv.1706.07100,
  title  = {Solution of parabolic free boundary problems using transmuted heat polynomials},
  author = {Igor V. Kravchenko and Vladislav V. Kravchenko and Sergii M. Torba},
  journal= {arXiv preprint arXiv:1706.07100},
  year   = {2017}
}

Comments

14 pages, 4 figures, contact details updated

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