Table 1 Error results of finite difference method and Galerkin finite element method
From: A numerical solution of a singular boundary value problem arising in boundary layer theory
\(\beta \) | \(\lambda \) | |||||
|---|---|---|---|---|---|---|
\(-\)0.10 | \(-\)0.15 | \(-\)0.18 | \(-\)0.20 | \(-\)0.25 | \(-\)0.30 | |
0 | \(2.985\times {10^{-6}}\) | \(3.433\times {10^{-6}}\) | \(3.780\times {10^{-6}}\) | \(4.051\times {10^{-6}}\) | \(4.892\times {10^{-6}}\) | \(5.427\times {10^{-6}}\) |
0.1 | \(3.010\times {10^{-6}}\) | \(3.465\times {10^{-6}}\) | \(3.818\times {10^{-6}}\) | \(4.096\times {10^{-6}}\) | \(4.976\times {10^{-6}}\) | \(5.882\times {10^{-6}}\) |
0.2 | \(3.074\times {10^{-6}}\) | \(3.543\times {10^{-6}}\) | \(3.910\times {10^{-6}}\) | \(4.202\times {10^{-6}}\) | \(5.167\times {10^{-6}}\) | \(6.962\times {10^{-6}}\) |
0.3 | \(3.174\times {10^{-6}}\) | \(3.664\times {10^{-6}}\) | \(4.051\times {10^{-6}}\) | \(4.364\times {10^{-6}}\) | \(5.452\times {10^{-6}}\) | \(8.674\times {10^{-5}}\) |
0.5 | \(3.516\times {10^{-6}}\) | \(4.076\times {10^{-6}}\) | \(4.532\times {10^{-6}}\) | \(4.913\times {10^{-6}}\) | \(6.419\times {10^{-6}}\) | \(1.540\times {10^{-5}}\) |
0.7 | \(4.270\times {10^{-6}}\) | \(4.993\times {10^{-6}}\) | \(5.609\times {10^{-6}}\) | \(6.151\times {10^{-6}}\) | \(8.662\times {10^{-6}}\) | \(4.706\times {10^{-5}}\) |
0.9 | \(7.320\times {10^{-6}}\) | \(8.807\times {10^{-6}}\) | \(1.021\times {10^{-5}}\) | \(1.157\times {10^{-5}}\) | \(1.993\times {10^{-5}}\) | \(1.303\times {10^{-4}}\) |