Design and Numerical Solutions of a Novel Third-Order Nonlinear Emden–Fowler Delay Differential Model

Table 1

Comparison of the obtained results from GA-ASM for solving the nonlinear EF-DD model based on both problems of type 1.

	Problem I			Problem 2
	Exact	GA-ASM	AE	Exact	GA-ASM	AE
0	1.00000000	0.99998788	1.212101E − 05	1.00000000	0.99999570	4.2979068E − 06
0.05	1.00012500	1.00010387	2.112830E − 05	1.00000026	0.99999586	4.4025337E − 06
0.1	1.00100000	1.00097307	2.693406E − 05	1.00000417	0.99999959	4.5773499E − 06
0.15	1.00337500	1.00335045	2.454778E − 05	1.00002108	1.00001622	4.8547562E − 06
0.2	1.00800000	1.00799333	6.670848E − 06	1.00006658	1.00006131	5.2678390E − 06
0.25	1.01562500	1.01566134	3.633505E − 05	1.00016242	1.00015658	5.8417298E − 06
0.3	1.02700000	1.02711600	1.160012E − 04	1.00033649	1.00032991	6.5812201E − 06
0.35	1.04287500	1.04311966	2.446627E − 04	1.00062271	1.00061526	7.4548770E − 06
0.4	1.06400000	1.06443360	4.336027E − 04	1.00106099	1.00105262	8.3764421E − 06
0.45	1.09112500	1.09181538	6.903829E − 04	1.00169710	1.00168792	9.1849453E − 06
0.5	1.12500000	1.12601542	1.015419E − 03	1.00258256	1.00257294	9.6257224E − 06
0.55	1.16637500	1.16777299	1.397990E − 03	1.00377452	1.00376519	9.3353752E − 06
0.6	1.21600000	1.21781202	1.812016E − 03	1.00533561	1.00532778	7.8346627E − 06
0.65	1.27462500	1.27683704	2.212044E − 03	1.00733380	1.00732926	4.5343334E − 06
0.7	1.34300000	1.34552994	2.529940E − 03	1.00984219	1.00984343	1.2400050E − 06
0.75	1.42187500	1.42454775	2.672747E − 03	1.01293887	1.01294907	1.0196762E − 05
0.8	1.51200000	1.51452198	2.521980E − 03	1.01670671	1.01672970	2.2992646E − 05
0.85	1.61412500	1.61605929	1.934293E − 03	1.02123315	1.02127325	4.0102911E − 05
0.9	1.72900000	1.72974297	7.429666E − 04	1.02660997	1.02667161	6.1637149E − 05
0.95	1.85737500	1.85613407	1.240925E − 03	1.03293309	1.03302018	8.7089331E − 05
1	2.00000000	1.99577063	4.229373E − 03	1.04030231	1.04041732	1.1501021E − 04