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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