Two Simple Numerical Methods for the Free Boundary in One-Phase Stefan Problem

Table 1

Values in the solution.

Safety parameter 𝜌	RMSE	𝑆(𝑡=0.5)	𝑢(0.5,𝑇)	𝑢(1.0,𝑇)	𝑢(1.5,𝑇)
0.0060	0.000407836	1.4998795	3.4807649	1.7177973	0.6484301
0.0062	0.000407824	1.4998786	3.4807643	1.7177965	0.6484289
0.0064	0.000407814	1.4998777	3.4807638	1.7177957	0.6484277
0.0066	0.000407806	1.4998767	3.4807632	1.7177949	0.6484264
0.0068	0.000407802	1.4998758	3.4807627	1.7177941	0.6484252
0.0070	0.000407799	1.4998748	3.4807621	1.7177933	0.6484240
0.0072	0.000407800	1.4998739	3.4807616	1.7177925	0.6484227
0.0074	0.000407803	1.4998729	3.4807610	1.7177917	0.6484215
0.0076	0.000407809	1.4998720	3.4807604	1.7177909	0.6484203
0.0078	0.000407817	1.4998711	3.4807599	1.7177901	0.6484190
0.0080	0.000407828	1.4998702	3.4807594	1.7177893	0.6484178
Maximum difference	0.000000037	0.0000093	0.0000055	0.0000080	0.0000123