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Theory and Modern Applications

Table 5 (Example 6.2) \(E_{2}(h,\tau )\), \(E_{\infty }(h,\tau )\) and spatial convergence orders

From: Quintic non-polynomial spline for time-fractional nonlinear Schrödinger equation

γ

h

\(E_{2}(h,\tau )\)

Space2

\(E_{\infty }(h,\tau )\)

\(\text{Space}_{\infty }\)

\(E_{\infty }(h,\tau )\)

\(\text{Space}_{\infty }\)

Our method

Our method

CNS [36]

0.3

1/5

1.0859e−02

 

1.5317e−02

 

2.6918e−02

 

1/10

5.7585e−05

7.5590

7.7577e−05

7.6253

1.6327e−03

4.0432

1/20

7.3933e−07

6.2833

1.0550e−06

6.2003

1.0095e−04

4.0155

0.5

1/5

1.0808e−02

 

1.5308e−02

 

2.6893e−02

 

1/10

5.7103e−05

7.5643

7.6944e−05

7.6363

1.6200e−03

4.0532

1/20

7.3204e−07

6.2855

1.0429e−06

6.2051

1.0053e−04

4.0103

0.7

1/5

1.0698e−02

 

1.5253e−02

 

2.6736e−02

 

1/10

5.6084e−05

7.5755

7.5675e−05

7.6551

1.5956e−03

4.0666

1/20

7.6999e−07

6.1866

1.2828e−06

5.8824

9.9461e−05

4.0038