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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