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Theory and Modern Applications

Table 1 Example 2: Maximum absolute errors \(\pmb{e_{m,\infty}}\) with \(\pmb{m=5 }\) , \(\pmb{\alpha=0.4 }\) , \(\pmb{\beta =0.4}\) and \(\pmb{L=3}\)

From: On a hybrid spectral exponential Chebyshev method for time-fractional coupled Burgers equations on a semi-infinite domain

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TQF

\(O(\tau^{2})\)

FDM

\(O(\tau^{2-\alpha})\)

\(e_{5,\infty}(u)=e_{5,\infty}(v)\)

\(e_{5,\infty}(u)=e_{5,\infty }(v)\)

0.015625

1.62969572 × 10−3

 

1.58537183 × 10−2

 

0.0078125

4.07935306 × 10−4

1.99

5.42638453 × 10−3

1.54

0.00390625

9.40924121 × 10−5

2.01

1.82754471 × 10−3

1.57

0.001953125

1.58381076 × 10−5

2.07

6.04886113 × 10−4

1.55