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Theory and Modern Applications

Table 5 The error of two different schemes for \(\mathrm{SP} _{3}\) at \(t=2\)

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

\(({x_{i}},{y_{i}})\)

CFDS6-SSM

E-CFDS6-SSM

DADI (error)

(0.2Ï€, 0.2Ï€)

8.6691e−09

8.6716e−09

9.0752e−04

(0.4Ï€, 0.4Ï€)

2.2696e−08

2.2699e−08

2.3615e−03

(0.6Ï€, 0.6Ï€)

2.2696e−08

2.2699e−08

2.3437e−03

(0.8Ï€, 0.8Ï€)

8.6691e−09

8.6716e−09

8.8970e−04

Nodes

41 × 41

41 × 41

201 × 201