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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)
(0.2π, 0.2π) 8.6691e−09 8.6716e−09 9.0752e−04
(0.4π, 0.4π) 2.2696e−08 2.2699e−08 2.3615e−03
(0.6π, 0.6π) 2.2696e−08 2.2699e−08 2.3437e−03
(0.8π, 0.8π) 8.6691e−09 8.6716e−09 8.8970e−04
Nodes 41 × 41 41 × 41 201 × 201