Logistic Heat Integral Methods for the One-Phase Stefan Problem

Table 3

𝐿²-norm-type error comparison of Gaussian and logistic HBIM and RIM temperature estimates for (1.1) and (1.2) over domain (𝑥,𝑡)∈(0,𝛿(𝑡))×[0,1].

	Θ(𝑥,𝑡) errors
𝛽	Gaussian HBIM	Gaussian RIM	LHBIM	LRIM
1	1.4421×10^−5	8.0325×10^−4	2.7660×10^−5	5.6510×10^−4
1.25	1.2284×10^−5	5.5010×10^−4	1.9031×10^−5	3.9086×10^−4
1.67	8.8848×10^−6	3.2795×10^−4	1.1350×10^−5	2.3563×10^−4
2.5	4.9245×10^−6	1.5296×10^−4	5.2625×10^−6	1.1128×10^−4
5	1.4269×10^−6	3.7774×10^−5	1.2800×10^−6	2.7874×10^−5
10	3.5314×10^−7	8.6657×10^−6	2.8998×10^−7	6.4450×10^−6