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Theory and Modern Applications

Table 9 The convergence order and computational time for \(\mathrm {SP} _{6}\) at \(t=1\)

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

 

Nodes

21 × 21 × 21

41 × 41 × 41

81 × 81 × 81

CFDS6-SSM

Max (error)

3.9145e−04

7.0154e−06

1.1455e−07

Time (s)

20.035465

45.750996

90.070817

Order

5.802

5.936

E-CFDS6-SSM

Max (error)

3.9128e−04

7.0141e−06

1.1455e−07

Time (s)

5.032226

10.448344

23.028154

Order

5.801

5.936