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Theory and Modern Applications

Table 2 The error comparison between CFDS-PIM and the other method at \(t=2\). N is the number of points of the one-dimensional mesh in case 1 of Example 1

From: A new high-order compact finite difference scheme based on precise integration method for the numerical simulation of parabolic equations

 

CFDS-PIM

Ref. [1]

Taylor

Padé

\(x_{i}\)

0.2

3.002 × 10−10

1.799 × 10−10

2.251 × 10−3

0.4

4.821 × 10−10

2.874 × 10−10

3.364 × 10−3

0.6

4.821 × 10−10

2.874 × 10−10

3.364 × 10−3

0.8

3.002 × 10−10

1.799 × 10−10

2.251 × 10−3

N

 

41

41

101