Theory and Modern Applications
Table 5 The results obtained for \(\mathfrak{J}\) and CPU time with \(\alpha =1\) via several numerical schemes for Example 1
Method | \(\mathfrak{J}\) | CPU Time |
|---|---|---|
Hybrid of block-pulse and Bernoulli polynomials [44] | Â | Â |
\(M_{1}=3\) and \(N_{1}=1\) | 0.1929094450245 | 4.79688 |
\(M_{1}=5\) and \(N_{1}=1\) | 0.1929092980929 | 6.25000 |
Hybrid of block-pulse functions and Taylor polynomials [45] | Â | Â |
\(M_{2}=3\) and \(N_{1}=1\) | 0.1929094450240 | 2.42188 |
\(M_{2}=5\) and \(N_{1}=1\) | 0.1929092980930 | 3.73225 |
The proposed method | Â | Â |
N = 3 | 0.1929250524756 | 0.469 |
N = 5 | 0.1929092986997 | 0.484 |
N = 7 | 0.1929092980932 | 0.500 |
Exact | 0.1929092980932 | Â |