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Theory and Modern Applications

Table 1 Comparisons of errors and CPU time of the CCNFD and OCNFDE solutions

From: An optimized Crank–Nicolson finite difference extrapolating model for the fractional-order parabolic-type sine-Gordon equation

Real time

CCNFD scheme

OCNFDE scheme

Error \(\|\tilde{\boldsymbol{V}}(t_{n})-\boldsymbol{V}^{n}\|_{2}\)

CPU time

Error \(\|\tilde{\boldsymbol{V}}(t_{n})-\boldsymbol{V}_{d}^{n}\|_{2}\)

CPU time

n = 100,000

0.00046

381 s

0.00048

3.0 s

n = 150,000

0.00058

571 s

0.00063

4.5 s

n = 200,000

0.00076

762 s

0.00082

6.0 s