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Theory and Modern Applications

Table 5 Numerical results of one-dimensional parabolic problem with variable coefficients at \(t=0.1\) for Example 2

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

 

N

11

21

41

81

Taylor

Max(error)

1.894 × 10−6

5.216 × 10−9

3.264 × 10−11

1.663 × 10−12

CPU (s)

0.270

0.278

0.325

0.522

Order

8.529

7.295

4.295

Padé

Max(error)

1.894 × 10−6

5.216 × 10−9

3.081 × 10−11

3.132 × 10−13

CPU (s)

0.266

0.283

0.319

0.576

Order

8.504

7.403

6.620