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Theory and Modern Applications

Table 2 The convergence order and computational time for \(\mathrm {SP} _{1}\) at \(t=1\)

From: An efficient high-order compact finite difference scheme based on proper orthogonal decomposition for the multi-dimensional parabolic equation

 

Nodes

11 × 11

21 × 21

41 × 41

CFDS6-SSM

Max (error)

0.0441

2.1770e−04

1.3977e−06

Time (s)

10.099649

126.587866

416.107510

Order

7.662

7.283

E-CFDS6-SSM

Max (error)

0.0197

5.9319e−05

1.1370e−06

Time (s)

1.091099

51.221890

234.497833

Order

8.375

5.705