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Table 2 Comparison of exact and approximate solution of Example  1 using the boundary condition as defined in \(\pmb{\mathbf{S_{1}}}\)

From: Approximate solution of linear and nonlinear fractional differential equations under m-point local and nonlocal boundary conditions

  \(\boldsymbol {S_{1}}\) \(\boldsymbol {S_{2}}\)
  \(\boldsymbol {\|E_{N}\|_{2}}\) \(\boldsymbol {\|E_{N}\|_{\infty}}\) \(\boldsymbol {\|E_{N}\| _{2}}\) \(\boldsymbol {\|E_{N}\|_{\infty}}\)
N = 5 7.23 × 10−2 6.53 × 10−1 4.72 × 10−1 3.68 × 10−1
N = 8 1.003 × 10−4 2.913 × 10−2 6.53 × 10−2 0.58 × 10−3
N = 10 4.82 × 10−6 3.21 × 10−5 0.587 × 10−3 0.778 × 10−4
N = 15 3.92 × 10−11 7.84 × 10−9 9.51 × 10−5 9.510 × 10−8
N = 20 6.22 × 10−16 5.61 × 10−14 1.51 × 10−10 1.456 × 10−12
N = 30 9.36 × 10−19 8.22 × 10−18 9.510 × 10−11 9.108 × 10−13
N = 40 9.28 × 10−21 0.781 × 10−18 5.87 × 10−16 5.33 × 10−18