A Method for Solving Moving Boundary Problems in Heat Flow using Cubic Splines or Polynomials

Abstract

A new approach to a heat-flow problem involving a moving boundary makes use of a grid system which moves with the boundary. Two variations of the method are described. In the first, necessary interpolations are performed by using cubic splines; in the second, cubic polynomials are employed. The method smooths out irregularities in the motion of the boundary which were evident in previous calculations based on a fixed grid system.