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Theory and Modern Applications

Table 7 The maximum error and convergence rate for Problem 1, Problem 2 with \(\varepsilon = 10^{ - 1}\) and Problem 3 with \(\operatorname{Re}=10\)

From: A higher-order blended compact difference (BCD) method for solving the general 2D linear second-order partial differential equation

\(h_{x}\)

\(h_{y}\)

Problem 1

Problem 2

Problem 3

Error

Rate

Error

Rate

Error

Rate

1/16

1/8

1.84(−08)

 

3.85(−05)

 

6.15(−05)

 

1/32

1/16

1.87(−10)

6.62

5.14(−07)

6.23

8.95(−07)

6.10

1/64

1/32

1.88(−12)

6.63

4.80(−09)

6.74

8.56(−09)

6.71

1/8

1/16

1.76(−06)

 

3.85(−05)

 

6.27(−05)

 

1/16

1/32

2.09(−08)

6.40

5.14(−07)

6.23

7.47(−07)

6.39

1/32

1/64

2.97(−10)

6.14

4.59(−09)

6.81

7.85(−09)

6.57