Solution of parabolic free boundary problems using transmuted heat polynomials

Generalized exponential basis for efficient solving of homogeneous diffusion free boundary problems: Russian option pricing

“…The theorem provides tools for computation of the transmuted powers. It was used directly in Kravchenko et al (2017a) for the application of the Transmuted heat polynomials (THP) method to the Stefan-like problem. In this paper, we will use a different CSS.…”

“…We can choose a more general representation for the boundary if needed. See Kravchenko et al (2017a) for the discussion.…”

“…This reformulation of the problem leads to a more robust convergence of the numerical method-see Herrera-Gomez and Porter (2017). We will apply this technique to the FHRO in Section 7-see also Kravchenko et al (2017a) for details in the THP case.…”

“…For the implementation details of the first two steps of the proposed algorithm, i.e., construction of a particular solution f and of the coefficients α n and µ n we refer the reader to Kravchenko et al (2017b), Kravchenko and Torba (2018), Kravchenko et al (2017a) and only want to mention that since the maximum upper boundary b ∞ is known-see Appendix A.1, we only need values of E ± n (y) on the interval [0, b ∞ ]. In our computations we have used this knowledge and chose the interval [0, L] to be a bit larger than [0, b ∞ ].…”

“…In Kravchenko et al (2017a), a numerical method was developed for the classical one dimensional Stefan like problem for the time-homogeneous parabolic operator using the CSS of the transmuted heat polynomials, that was referred to as THP method. It is well known that the CSS based on polynomials result in badly conditioned matrices, making the application of THP complicated for the practical computations.…”