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

Table 3

The maximum norm error and the temporal accuracy of 𝑢^𝑛_𝑖,𝑗 for Example 5.

𝜏	𝐿1-ADI scheme (ℎ=1/200)			BD-ADI scheme (ℎ=1/200)
	𝛼	error(𝜏,ℎ)	order(𝜏)	𝛼	error(𝜏,ℎ)	order(𝜏)
1/20	1/2	4.6386801902𝑒−03	0.835782	1/3	3.0682418814𝑒−03	1.247710
1/40		2.5989567998𝑒−03	0.906370		1.2920863692𝑒−03	1.295329
1/80		1.3866102907𝑒−03	0.947443		5.2645185538𝑒−04	1.315075
1/160		7.1902789341𝑒−04	0.970534		2.1158337290𝑒−04	1.325682
1/320		3.6693233527𝑒−04	0.983962		8.4413446753𝑒−05	1.335982
1/640		1.8551714096𝑒−04			3.3438043901𝑒−05
1/20	2/3	1.5621553331𝑒−03	1.192172	1/2	1.5491678500𝑒−03	1.423830
1/40		6.8366714097𝑒−04	1.262779		5.7740819917𝑒−04	1.463914
1/80		2.8491177407𝑒−04	1.297640		2.0931522211𝑒−04	1.481554
1/160		1.1589959988𝑒−04	1.317329		7.4956359178𝑒−05	1.496663
1/320		4.6507867889𝑒−05	1.333601		2.6562452368𝑒−05	1.524750
1/640		1.8453234155𝑒−05			9.2315064167𝑒−06
1/20	3/4	1.7962917770𝑒−03	1.063599	2/3	1.1129679333𝑒−03	1.112230
1/40		8.5941268352𝑒−04	1.128142		5.1483494465𝑒−04	1.171085
1/80		3.9318529135𝑒−04	1.161548		2.2863166690𝑒−04	1.211600
1/160		1.7576660520𝑒−04	1.180856		9.8720772742𝑒−05	1.239224
1/320		7.7528818903𝑒−05	1.191836		4.1818156321𝑒−05	1.255314
1/640		3.3937881480𝑒−05			1.7517727276𝑒−05