Research Article
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 |
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Bold values represent the overall mean for MSE.
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