High order locally one-dimensional methods for solving two-dimensional parabolic equations

Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 4 \(L^{2} \)-norm error and convergence rate for Problem 2 with \(h = \tau\) at \(T = 1\)

h	P–R scheme		Fourth order scheme (22)		Sixth order scheme (33)
h	Error	Rate	Error	Rate	Error	Rate
1/10	1.08(−2)		7.36(−3)		1.31(−3)
1/20	1.08(−2)	0.00	4.57(−4)	4.01	2.15(−5)	5.92
1/30	5.03(−3)	1.88	8.95(−5)	4.02	1.91(−6)	5.97
1/40	2.84(−3)	1.99	2.82(−5)	4.01	3.40(−7)	5.99