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Theory and Modern Applications

Table 15 \(L_{2}\) and \(L_{\infty }\) error norms for \(u(x,t)=v(x,t)\) of Example 3 when \(0\leq x\leq 3\), \(\alpha _{1}=\alpha _{2}=0.01\)

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

2.000018 × 10−4

1.55667 × 10−4

15

9.35962 × 10−7

7.7069 × 10−7

6

1.597 × 10−5

1.258 × 10−5

18

3.955739 × 10−7

3.25713 × 10−7

8

8.652582 × 10−8

5.769225 × 10−8

21

1.529046 × 10−7

1.25894 × 10−7

10

3.859747 × 10−10

3.023012 × 10−10

25

5.536353 × 10−9

3.76237 × 10−9