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Theory and Modern Applications

Table 20 \(L_{2}\) and \(L_{\infty }\) error norms for \(u(x,t)=v(x,t)\) of Example 3 when \(0\leq x\leq 1\), \(\alpha _{1}=\alpha _{2}=0.6\)

From: Non-polynomial B-spline and shifted Jacobi spectral collocation techniques to solve time-fractional nonlinear coupled Burgers’ equations numerically

SJSCM (μ = η = 0, M = N)

Non-polynomial, k = 1/512

N

\(L_{2}(U)=L_{2}(V)\)

\(L_{\infty }(U)=L_{\infty }(V)\)

N

\(L_{2}(U)=L_{2}(V)\)

\(L_{\infty }(U)=L_{\infty }(V)\)

5

1.0633419 × 10−4

1.32559 × 10−4

6

6.033058 × 10−5

8.22097 × 10−5

6

1.342882 × 10−8

1.3744817 × 10−8

8

6.03903 × 10−5

8.24068 × 10−5

8

6.013554 × 10−10

8.475583 × 10−10

10

6.040936 × 10−5

8.24265 × 10−5

10

3.003675 × 10−11

4.244149 × 10−11

12

6.041691 × 10−5

8.23957 × 10−5