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Table 2 Numerical results of \(\mathrm{SP} _{1}\) at \(t = 2\), with \(h=0.01\pi \), \(\tau =0.0025\)

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

x

Exact

R-CFDS4

Error (R-CFDS4)

CFDS4

Error (CFDS4)

0.2Ï€

0.079548

0.079548

8.2217e − 08

0.079548

8.2217e − 08

0.4Ï€

0.128712

0.128711

1.3303e − 07

0.128711

1.3303e − 07

0.6Ï€

0.128712

0.128711

1.3303e − 07

0.128711

1.3303e − 07

0.8Ï€

0.079548

0.079548

8.2217e − 08

0.079548

8.2217e − 08

Time

 

0.126824 s

 

49.099276 s

Â