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. 2026 Jan 21;16:5964. doi: 10.1038/s41598-026-36463-9

Table 2.

Problem 7.1: Convergence in space of the proposed scheme using time step size Inline graphic.

Values of Inline graphic h Error Order-Inline graphic CPU Time
Inline graphic 0.10000 3.0431e-04 0.0000 0.0699
0.05000 4.4229e-05 2.7824 0.0485
0.02500 5.7438e-06 2.9449 0.0528
0.01250 7.2755e-07 2.9809 0.0641
0.00625 9.2607e-08 2.9738 0.0824
0.00313 1.2309e-08 2.9114 0.1140
Inline graphic 0.10000 3.5492e-04 0.0000 0.0708
0.05000 5.1581e-05 2.7826 0.0511
0.02500 6.6959e-06 2.9455 0.0539
0.01250 8.4687e-07 2.9831 0.0628
0.00625 1.0715e-07 2.9824 0.0813
0.00313 1.3928e-08 2.9437 0.1091
Inline graphic 0.10000 3.9538e-04 0.0000 0.0719
0.05000 5.7447e-05 2.7829 0.0524
0.02500 7.4503e-06 2.9469 0.0533
0.01250 9.3870e-07 2.9886 0.0671
0.00625 1.1698e-07 3.0044 0.0869
0.00313 1.4318e-08 3.0304 0.1081