Skip to main content

Theory and Modern Applications

Table 7 Numerical results of two-dimensional parabolic problem with time step size \(\tau= 5 \times{10^{- 5}}\) at \(t=0.1\) for case 2 of Example 4

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

 

N

11 × 11

21 × 21

41 × 41

81 × 81

Taylor

Max(error)

1.213 × 10−6

3.481 × 10−9

2.183 × 10−11

2.574 × 10−13

CPU (s)

0.022

0.034

0.036

0.043

Order

6.313

9.562

8.000

Padé

Max(error)

1.213 × 10−6

3.352 × 10−9

1.072 × 10−11

1.286 × 10−10

CPU (s)

0.016

0.038

0.042

0.041

Order

8.500

8.289

−0.263