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Table 16 Numerical results of \(\mathrm{SP} _{4}\) at \(t=2\), with \(h = 0.02\pi \), \(\tau = 0.02\)

From: A reduced fourth-order compact difference scheme based on a proper orthogonal decomposition technique for parabolic equations

(x,y)

Exact

R-ADI-CFDS4

Error 1

ADI-CFDS4

Error 2

(0.2Ï€,0.2Ï€)

0.046757

0.046758

6.7914e − 07

0.046758

6.7914e − 07

(0.4Ï€,0.4Ï€)

0.122412

0.122414

1.7780e − 06

0.122414

1.7780e − 06

(0.6Ï€,0.6Ï€)

0.122412

0.122414

1.7780e − 06

0.122414

1.7780e − 06

(0.8Ï€,0.8Ï€)

0.046757

0.046758

6.7914e − 07

0.046758

6.7914e − 07

Time

 

0.361219 s

 

80.801341 s

Â