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Advances in Continuous and Discrete Models

Theory and Modern Applications

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

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

h

P–R scheme

Fourth order scheme (22)

Sixth order scheme (33)

Error

Rate

Error

Rate

Error

Rate

1/10

1.09(−9)

 

3.84(−11)

 

2.39(−13)

 

1/20

4.16(−10)

1.39

2.28(−12)

4.07

3.62(−15)

6.04

1/30

2.01(−10)

1.79

4.46(−13)

4.02

3.15(−16)

6.02

1/40

1.16(−10)

1.91

1.41(−13)

4.00

5.55(−17)

6.04

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