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Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 2 \(L^{2}\)-error and convergence rate for Problem 1 with \(h = 0.02\) at \(T = 1\)

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

τ

P–R scheme

Fourth order scheme (22)

Sixth order scheme (33)

Error

Rate

Error

Rate

Error

Rate

1/10

7.89(−9)

 

3.37(−11)

 

2.51(−13)

 

1/20

1.16(−9)

2.76

2.21(−12)

3.93

3.83(−15)

6.03

1/30

4.00(−10)

2.62

4.34(−13)

4.01

3.48(−16)

5.92

1/40

1.93(−10)

2.53

1.38(−13)

3.98

5.77(−17)

6.25

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