Special Functions and HHL Quantum Algorithm for Solving Moving Boundary Value Problems Occurring in Electric Contact Phenomena

This series of studies is devoted to developing and employing mathematical methods along with quantum algorithms for solving moving boundary value problems which occur in heat and mass transfer problems. In this particular study we develop mathematical framework where we utilize special functions and Harrow-Hassidim-Lloyd (HHL) quantum algorithm for finding exact and approximate solutions of Generalized Heat Equation with moving boundaries and as examples we consider plane and spherical cases. In spherical case the Generalized Heat Equation is reduced to linear moving boundary value problem with discontinuous coefficients and solved exactly. In plane case we use collocation method for approximate solution of Inverse Two-Phase Stefan problem. Experimental verification of suggested mathematical framework has been tested for modeling arcing phenomena in composite electrical contacts with AgCdO (90%) and Ni (10%). HHL algorithm was applied and run on IBM Q with Qiskit and the code is openly available on https://github.com/users/Schrodinger-cat-kz/projects/2.