TITLE:
Approximate Analytical Solutions to the Heat and Stokes Equations on the Half-Line Obtained by Fokas’ Transform
AUTHORS:
Mohamed Lachaab, Marius Beceanu
KEYWORDS:
Heat Equation, Stokes Equation, Fokas’ Transform, Asymptotic Expansion, Hilbert Transform, Incomplete Airy Function, Imaginary Error Function
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.9 No.4,
April
29,
2021
ABSTRACT: In this paper, we evaluate the integrals that are solutions of the heat and Stokes’ equations obtained by Fokas’ transform method by deriving exact formulas. Our method is more accurate and efficient than the contour deformation and parametrization used by Fokas to compute these integrals. In fact, for the heat equation, our solution is exact up to the imaginary error function and for the Stokes equation, our solution is exact up to the incomplete Airy function. In addition, our solutions extend to the lateral boundary without convergence issues, allow for asymptotic expansions, and are much faster than those obtained by other methods.