Approximate Solutions of Mathematical Models of Supercooling Solidification

Abstract

In [1], [2], some one-dimensional mathematical models of supercooling solidification have been established, and some existence theorems have been proven by a difference method. In this paper, the models and the method are shown again in §§ 1, 2 and another analytic method of approximate solution is proposed in § 3. It is based on the assumption that a profile of temperature distribution at any time may be considered linear in every inner region. By some numerical examples, solutions by the approximate method are compared with some solutions given by the difference method. It is then realized that the approximate solutions come sufficiently close to the difference solutions.