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

TL;DR

This paper explores the application of special functions and the HHL quantum algorithm to solve moving boundary heat transfer problems in electric contact phenomena, providing exact and approximate solutions for complex geometries.

Contribution

It introduces the use of the HHL quantum algorithm for solving generalized heat equations with moving boundaries, including cases with discontinuous coefficients.

Findings

Exact solution for spherical moving boundary problem.

Approximate solution for plane inverse Stefan problem.

Demonstrates quantum algorithm's effectiveness in boundary value problems.

Abstract

This is a series of studies devoted to modeling and solving heat and mass transfer problems occurring in electric contacts where we employ and develop mathematical apparatus along with quantum algorithms for solving moving boundary value problems. In this particular study we utilize special functions and demonstrate the use of 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.