Table 1 The exact and NITM results of \(\mu (\zeta ,\varphi ,\Im )\) and absolute error of Example 1.
From: Analysis of some dynamical systems by combination of two different methods
\(({\zeta ,{\varphi }})\) | \(u({\zeta ,{\varphi }})\)at \({ \varpi }=\)0.5 | \(\mu ({\zeta ,{\varphi }})\)at \({ \varpi }=\)0.75 | \(\mu ({\zeta ,{\varphi }})\)at \({ \varpi }=\)1 | Exact | Absolute error Of HPM26 | Absolute error NITM solution |
|---|---|---|---|---|---|---|
(0.1,0.1) | 0.500817 | 0.500795 | 0.500782 | 0.500782 | 1.07078\({ \times }10^{-11}\) | 1.67111\({ \times }10^{-12}\) |
(0.1,0.3) | 0.500853 | 0.500829 | 0.50081 | 0.50081 | 3.04565\({ \times }10^{-9}\) | 4.51196\({ \times }10^{-11}\) |
(0.1,0.5) | 0.500878 | 0.500857 | 0.500837 | 0.500837 | 4.81303\({ \times }10^{-8}\) | 2.08888\({ \times }10^{-10}\) |
(0.2,0.1) | 0.49812 | 0.498098 | 0.498085 | 0.498085 | 1.04388\({ \times }10^{-11}\) | 1.57879\({ \times }10^{-12}\) |
(0.2,0.3) | 0.498154 | 0.498131 | 0.498112 | 0.498112 | 2.97260\({ \times }10^{-10}\) | 4.26227\({ \times }10^{-11}\) |
(0.2,0.5) | 0.498178 | 0.498158 | 0.498139 | 0.498139 | 4.70138\({ \times }10^{-9}\) | 1.97328\({ \times }10^{-10}\) |
(0.3,0.1) | 0.495491 | 0.49547 | 0.495458 | 0.495458 | 1.01776\({ \times }10^{-11}\) | 1.49181\({ \times }10^{-12}\) |
(0.3,0.3) | 0.495525 | 0.495502 | 0.495484 | 0.495484 | 2.90150\({ \times }10^{-10}\) | 4.02799\({ \times }10^{-11}\) |
(0.3,0.5) | 0.495548 | 0.495529 | 0.49551 | 0.49551 | 2.90150\({ \times }10^{-10}\) | 4.02799\({ \times }10^{-11}\) |
(0.4,0.1) | 0.49293 | 0.492909 | 0.492897 | 0.492897 | 4.70138\({ \times }10^{-9}\) | 1.97328\({ \times }10^{-10}\) |
(0.4,0.3) | 0.492963 | 0.49294 | 0.492922 | 0.492922 | 9.92418\({ \times }10^{-12}\) | 1.41043\({ \times }10^{-12}\) |
(0.4,0.5) | 0.492985 | 0.492966 | 0.492948 | 0.492948 | 2.83229\({ \times }10^{-9}\) | 3.80803\({ \times }10^{-11}\) |
(0.5,0.1) | 0.490433 | 0.490413 | 0.490401 | 0.490401 | 2.76492\({ \times }10^{-10}\) | 3.60145\({ \times }10^{-11}\) |
(0.5,0.3) | 0.490465 | 0.490443 | 0.490426 | 0.490426 | 2.76492\({ \times }10^{-10}\) | 3.60145\({ \times }10^{-11}\) |
(0.5,0.5) | 0.490487 | 0.490469 | 0.490451 | 0.490451 | 4.38895\({ \times }10^{-9}\) | 1.66734\({ \times }10^{-10}\) |
