An approximate solution of fractional cable equation by homotopy analysis method

Boundary Value Problems

Table 3 Comparison of the HPM, HAM, exact solution (ES) and absolute errors results of $u (x, t)$ when $γ_{1} = γ_{2} = 0.25$ , $t = 0.1$ , and $h = - 0.004$ for 10th-order approximation

x	HPM	HAM	ES	Error (HPM)	Error (HAM)
0.1	−8614.19	0.00302986	0.00309017	8614.2	6.0306 × 10⁻⁵
0.2	−16385.2	0.00576314	0.00587785	16385.2	1.14709 × 10⁻⁵
0.3	−22552.2	0.00793229	0.00809017	22552.3	1.57883 × 10⁻⁴
0.4	−26511.8	0.00932496	0.00951057	26511.8	1.85603 × 10⁻⁴
0.5	−27876.1	0.00980485	0.01	27876.1	1.95154 × 10⁻⁴
0.6	−26511.8	0.00932496	0.00951057	26511.8	1.85603 × 10⁻⁴
0.7	−22552.2	0.00793229	0.00809017	22552.3	1.57883 × 10⁻⁴
0.8	−16385.2	0.00576314	0.00587785	16385.2	1.14709 × 10⁻⁵
0.9	−8614.19	0.00302986	0.00309017	8614.2	6.0306 × 10⁻⁵