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

Table 2

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

			ABSE		ABSE
−20	0.000000007610738	0.000000006675452	9.35286e − 10	0.000000008162226	0.000000e + 00
−18	0.000000056236173	0.000000049325291	6.91088e − 09	0.000000060311146	3.000000e − 15
−16	0.000000415532237	0.000000364467339	5.10649e − 08	0.000000445642439	1.520000e − 13
−14	0.000003070391012	0.000002693069248	3.77322e − 07	0.000003292876984	8.297000e − 12
−12	0.000022687291435	0.000019899092759	2.78820e − 06	0.000024331252426	4.530140e − 10
−10	0.000167637668860	0.000146977305345	2.06604e − 05	0.000179784855851	2.473371e − 08
−8	0.001238684022889	0.001074570778155	1.64113e − 04	0.001328416707133	1.350414e − 06
−6	0.009152658690634	0.007973830914374	1.17883e − 03	0.009817959806057	7.372924e − 05
−4	0.067610535301286	0.068261515182232	6.50980e − 04	0.072999276292701	4.022831e − 03
−2	0.492041285925229	0.524515277312650	3.24740e − 02	0.532436818143197	2.119519e − 01
0	1.993617022362784	1.999494403179591	5.87738e − 03	1.999999762175650	3.000000e + 00
2	0.574088616658195	0.539384921903072	3.47037e − 02	0.530772248534432	2.119531e − 01
4	0.079333147973226	0.078209018431132	1.12413e − 03	0.073476928282824	4.022874e − 03
6	0.010740723263978	0.011851152313279	1.11043e − 03	0.010011775130338	7.373004e − 05
8	0.001453609114015	0.001612040439639	1.58431e − 04	0.001355290064193	1.350429e − 06
10	0.000196724626664	0.000219748058095	2.30234e − 05	0.000183423393176	2.473398e − 08
12	0.000026623783132	0.000029747622897	3.12384e − 06	0.000024823678933	4.530190e − 10
14	0.000003603137231	0.000004025923061	4.22786e − 07	0.000003359519675	8.297000e − 12
16	0.000000487631598	0.000000544849488	5.72179e − 08	0.000000454661547	1.520000e − 13
18	0.000000065993760	0.000000073737360	7.74360e − 09	0.000000061531749	3.000000e − 15
20	0.000000008931284	0.000000009979266	1.04798e − 09	0.000000008327417	0.000000e + 00
MSE			1.0495530e − 03		8.93920866e − 05

Bold values represent the overall mean for MSE.