Skip to main content
Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 3 \(L^{2}\)-error and convergence rate for Problem 1 with \(\tau= 0.001\) 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

2.39(−10)

 

1.08(−12)

 

1.26(−14)

 

1/20

5.62(−11)

2.09

6.70(−14)

4.01

2.02(−16)

5.96

1/30

2.46(−11)

2.04

1.32(−14)

4.00

1.78(−17)

5.99

1/40

1.37(−11)

2.03

4.19(−15)

3.99

3.16(−18)

6.00

Back to article page