Improved Finite Difference Technique via Adomian Polynomial to Solve the Coupled Drinfeld’s–Sokolov–Wilson System

Table 1

Comparing the EFD and EFD-AP methods with the analytical solution for the DSW system for .

			ABSE		ABSE
−20	0.000000000000000	0.000000000000000	0.000000e + 00	0.000000000000000	0.000000e + 00
−18	0.000000000000002	0.000000000000002	0.000000e + 00	0.000000000000003	0.000000e + 00
−16	0.000000000000130	0.000000000000112	1.700000e − 14	0.000000000000152	1.000000e − 15
−14	0.000000000007070	0.000000000006119	9.520000e − 13	0.000000000008297	6.600000e − 14
−12	0.000000000386035	0.000000000334082	5.195200e − 11	0.000000000453014	3.607000e − 12
−10	0.000000021076791	0.000000018240133	2.836658e − 09	0.000000024733709	1.969470e − 10
−8	0.000001150753581	0.000000995445776	1.553078e − 07	0.000001350414470	1.075295e − 08
−6	0.000062828370830	0.000053705269772	9.123101e − 06	0.000073729242103	5.870768e − 07
−4	0.003428388362795	0.002899003871216	5.293845e − 04	0.004022830562664	3.201161e − 05
−2	0.181578470291215	0.181311969465876	2.665008e − 04	0.211951898242369	1.627998e − 03
0	2.980881623890990	2.999776943549420	1.889532e − 02	3.000000000312190	4.799980e − 05
2	0.247183304832390	0.242768208620821	4.415096e − 03	0.211953050552054	1.640126e − 03
4	0.004720311275506	0.005191658272445	4.713470e − 04	0.004022873546090	3.226855e − 05
6	0.000086522352175	0.000096544463815	1.002211e − 05	0.000073730044055	5.917936e − 07
8	0.000001584734592	0.000001782921624	1.981870e − 07	0.000001350429164	1.083933e − 08
10	0.000000029025434	0.000000032665115	3.639681e − 09	0.000000024733978	1.985290e − 10
12	0.000000000531619	0.000000000598286	6.666600e − 11	0.000000000453019	3.636000e − 12
14	0.000000000009737	0.000000000010958	1.221000e − 12	0.000000000008297	6.700000e − 14
16	0.000000000000178	0.000000000000201	2.200000e − 14	0.000000000000152	1.000000e − 15
18	0.000000000000003	0.000000000000004	0.000000e + 00	0.000000000000003	0.000000 + 00
20	0.000000000000000	0.000000000000000	0.000000e + 00	0.000000000000000	0.000000e + 00
MSE			3.807658e − 04		4.533085844e − 05

Bold values represent the overall mean for MSE.