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Theory and Modern Applications

Table 1 The error of two different schemes 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

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

CFDS6-SSM

E-CFDS6-SSM

DADI (error)

(0.4, 0.4)

1.0284e−06

1.2736e−06

1.5021e−02

(0.8, 0.8)

3.9282e−07

4.7769e−07

5.8051e−03

(1.2, 1.2)

3.9282e−07

4.7769e−07

5.5856e−03

(1.6, 1.6)

1.0284e−06

1.2736e−06

1.4801e−02

Nodes

41 × 41

41 × 41

201 × 201