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

Table 7

Comparison of VSG, BIM, LTUF, LTFF method, and exact solution when 𝑓(𝑡)=1.

position; 𝑥	Numerical solution				Exact; solution
	VSG	BIM	LTUF	LTFF
0.00	1.128379	1.128379	1.128379	1.128379	1.128379
0.10	1.030558	1.030846	1.031035	1.031171	1.031198
0.20	0.939323	0.939562	0.939461	0.938557	0.939644
0.30	0.853239	0.853118	0.852186	0.853340	0.853672
0.40	0.772252	0.772710	0.773105	0.772877	0.773215
0.50	0.696855	0.697913	0.698005	0.697264	0.698177
0.60	0.627581	0.628210	0.627142	0.628511	0.628436
0.70	0.563013	0.562986	0.563804	0.562138	0.563851
0.80	0.503018	0.503362	0.504110	0.504430	0.504255
0.90	0.447454	0.449016	0.448385	0.448748	0.448465
1.00	0.397071	0.398605	0.394381	0.399291	0.399282
1.10	0.351200	0.352020	0.353327	0.353470	0.353492
1.20	0.309050	0.310587	0.310942	0.311511	0.311870
1.30	0.270431	0.272901	0.274082	0.274519	0.274184
1.40	0.235147	0.238341	0.239877	0.239340	0.240196
1.50	0.203922	0.206799	0.208701	0.210078	0.209664
1.60	0.175475	0.179454	0.181921	0.182140	0.182347
1.70	0.149508	0.154482	0.157249	0.158290	0.158005
1.80	0.125812	0.131752	0.135028	0.136610	0.136403
1.90	0.104323	0.111398	0.116116	0.117326	0.117311
2.00	0.085031	0.093533	0.098785	0.100843	0.100509
RMSE	0.0055537	0.0024662	0.0007687	0.0006550
L2 norm	0.0789335	0.0350518	0.0109265	0.0093102
Runtime (secs)	0.795	0.860	0.783	0.821