Solution of parabolic free boundary problems using transmuted heat polynomials
arXiv:1706.0710010 citations
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For researchers in numerical PDEs, this offers a new approach to free boundary problems, but the results are theoretical without concrete numerical comparisons.
The paper proposes a numerical method for solving parabolic free boundary problems using transmuted heat polynomials, providing an efficient algorithm based on transmutation operator theory.
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.