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Solution of parabolic free boundary problems using transmuted heat polynomials
Author(s) -
Kravchenko Igor V.,
Kravchenko Vladislav V.,
Torba Sergii M.
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5483
Subject(s) - mathematics , boundary (topology) , boundary value problem , heat equation , construct (python library) , mathematical analysis , computer science , programming language
A numerical method for free boundary problems for the equationu x x − q ( x ) u = u tis proposed. The method is based on recent results from transmutation operators theory allowing one to construct efficiently a complete system of solutions for the above equation, generalizing the system of heat polynomials. The corresponding implementation algorithm is presented.