A New Legendre Collocation Method for Solving a Two-Dimensional Fractional Diffusion Equation

Table 2

Maximum absolute errors for problem (40) for 𝑇=1 and 𝑁=𝑀=12.

𝑥	𝑦	𝑡	𝐸(𝑥,𝑦,𝑡)	𝑥	𝑦	𝑡	𝐸(𝑥,𝑦,𝑡)	𝑥	𝑦	𝑡	𝐸(𝑥,𝑦,𝑡)
0.1	0.1	1	2.74515×10^−11	0.1	0.5	1	9.17923×10^−12	0.1	1	1	4.41521×10^−11
0.2			2.13241×10^−10	0.2			7.57278×10^−11	0.2			3.58585×10^−10
0.3			7.22081×10^−10	0.3			2.61927×10^−10	0.3			1.20622×10^−9
0.4			1.71192×10^−9	0.4			6.43406×10^−10	0.4			2.93613×10^−9
0.5			3.35365×10^−9	0.5			1.29893×10^−9	0.5			5.8445×10^−9
0.6			5.80344×10^−9	0.6			2.33485×10^−9	0.6			1.02404×10^−8
0.7			9.20721×10^−9	0.7			3.82976×10^−9	0.7			1.65193×10^−8
0.8			1.39884×10^−8	0.8			5.84963×10^−9	0.8			2.50569×10^−8
0.9			2.06847×10^−8	0.9			8.5766×10^−9	0.9			3.64012×10^−8
1			2.75218×10^−8	1			1.26484×10^−8	1			5.60815×10^−8