On a symbolic method for neutral functional-differential equations with proportional delays

Figures & data

Figure 1. Graphical results for Example, 3.1.

Figure 2. The absolute error $E_7$ for Example, 3.1.

Figure 3. Graphical results for Example, 3.3.

Table 1. Numerical results for Example, 3.1

$x$	Exact value $y(x)$	Approx. value $y(x)$	Absolute errors
$0.10$	$1.105170918$	$1.105170918$	$0$
$0.18$	$1.197217363$	$1.197217364$	$1.0\times {10}^{-9}$
$0.25$	$1.284025417$	$1.284025416$	$1.0\times {10}^{-9}$
$0.37$	$1.447734615$	$1.447734613$	$2.0\times {10}^{-9}$
$0.50$	$1.648721271$	$1.648721269$	$2.0\times {10}^{-9}$
$0.78$	$2.181472265$	$2.181472192$	$7.3\times {10}^{-8}$
$1.00$	$2.718281828$	$2.718281267$	$5.61\times {10}^{-7}$

Table 2. Numerical results for Example, 3.3

$x$	$E_4$	$E_5$	$E_6$
$0.20$	$4.09e-7$	$5.12e-8$	$6.40e-10$
$0.40$	$6.90e-6$	$8.63e-7$	$1.07e-7$
$0.60$	$3.69e-5$	$4.62e-6$	$5.78e-7$
$0.80$	$1.24e-4$	$1.55e-5$	$1.94e-6$
$1.00$	$3.25e-4$	$4.07e-5$	$5.09e-6$

Figure 4. Comparison of approximate and Exact solutions for Example 3.4.