Table 4 Comparison of \(E^{N,M}_{\varepsilon _{1},\varepsilon _{2}}, E^{N,M},{\overline{R}}^{N,M}\) for Example (1) with [9, 13]
\(\varepsilon _{2}=10^{-6}\) | \(N=32\) | \(N=64\) | \(N=128\) | \(N=256\) | \(N=512\) |
|---|---|---|---|---|---|
\(M=10\) | \(M=20\) | \(M=40\) | \(M=80\) | \(M=160\) | |
Present method | |||||
\(E^{N,M}\) | \(3.1504e-03\) | \(8.1321e-04\) | \(2.0669e-04\) | \(5.2043e-05\) | \(1.3070e-05\) |
\({\overline{R}}^{N,M}\) | 1.9538 | 1.9762 | 1.9906 | 1.9934 | − |
Result in [9](Exponentially Fitted Method) | |||||
\(E^{N,M}\) | \(3.9334e-03\) | \(1.1115e-03\) | \(2.9600e-04\) | \(7.6401e-05\) | \(1.9400e-05\) |
\({\overline{R}}^{N,M}\) | 1.8233 | 1.9088 | 1.9539 | 1.9775 | − |
Result in [13](Quadratic B-spline Collocation Method) | |||||
\(E^{N,M}\) | \(3.9420e-02\) | \(1.9392e-02\) | \(9.5791e-03\) | \(4.7594e-03\) | \(2.3718e-03\) |
\({\overline{R}}^{N,M}\) | 1.023 | 1.017 | 1.009 | 1.005 | − |