Maximum Norm Error Estimates of ADI Methods for a Two-Dimensional Fractional Subdiffusion Equation

Table 1

The maximum norm error and the temporal accuracy of 𝑢^𝑛_𝑖,𝑗 for Example 4.

𝜏	𝐿1-ADI scheme (ℎ=𝜋/200)			BD-ADI scheme (ℎ=𝜋/200)
	𝛼	error(𝜏,ℎ)	order(𝜏)	𝛼	error(𝜏,ℎ)	order(𝜏)
1/20	1/2	1.1393833280𝑒−03	0.860979	1/3	1.5093973350𝑒−03	1.266265
1/40		6.2732035469𝑒−04	0.882911		6.2750871863𝑒−04	1.285881
1/80		3.4017847773𝑒−04	0.910189		2.5735409495𝑒−04	1.301046
1/160		1.8101416127𝑒−04	0.936057		1.0444249965𝑒−04	1.319085
1/320		9.4608749632𝑒−05	0.959731		4.1859417673𝑒−05	1.351071
1/640		4.8643355059𝑒−05			1.6408936533𝑒−05
1/20	2/3	1.2585768427𝑒−03	1.260363	1/2	3.6622305737𝑒−04	1.463622
1/40		5.2537885652𝑒−04	1.288661		1.3278581143𝑒−04	1.474131
1/80		2.1505367805𝑒−04	1.303399		4.7796268443𝑒−05	1.488745
1/160		8.7133397922𝑒−05	1.307319		1.7030874694𝑒−05	1.514438
1/320		3.5208078966𝑒−05	1.297645		5.9613630191𝑒−06	1.535827
1/640		1.4322284746𝑒−05			2.0559641134𝑒−06
1/20	3/4	2.3004703569𝑒−03	1.174836	2/3	1.4653603051𝑒−03	1.207510
1/40		1.0189566568𝑒−03	1.197125		6.3452327488𝑒−04	1.242740
1/80		4.4441136189𝑒−04	1.210140		2.6813016026𝑒−04	1.264770
1/160		1.9208646006𝑒−04	1.216775		1.1158658090𝑒−04	1.276115
1/320		8.2643912130𝑒−05	1.217031		4.6074754492𝑒−05	1.274583
1/640		3.5550691871𝑒−05			1.9044750580𝑒−05