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Theory and Modern Applications

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

(0.2π, 0.2π)

1.3405e−06

1.3405e−06

8.4424e−5

(0.8π, 0.8π)

4.1228e−06

4.1230e−06

2.5983e−4

(1.2π, 1.2π)

4.1228e−06

4.1230e−06

2.5982e−4

(1.8π, 1.8π)

1.3396e−06

1.3405e−06

8.4416e−5

Nodes

41 × 41

41 × 41

201 × 201