A Comparison between Adomian Decomposition and Tau Methods

Table 1

Numerical results for Problem 2.

𝑠	Exact	Tau (𝑛)	ADM (𝜙)	Tau-Er.	ADM-Er.
𝑛=2,𝜙2
0.00	2.00000	1.99878	2.00000	1.2200𝑒−03	0.000𝑒+00
0.20	2.44000	2.43858	2.43989	1.4152𝑒−03	1.051𝑒−04
0.40	2.96000	2.95849	2.95782	1.5128𝑒−03	2.175𝑒−03
0.60	3.56000	3.55849	3.54811	1.5128𝑒−03	1.200𝑒−02
𝑛=5,𝜙3
0.00	2.00000	1.99885	2.00000	1.1525𝑒−03	0.000𝑒+00
0.20	2.44000	2.43867	2.44000	1.3342𝑒−03	2.228𝑒−06
0.40	2.96000	2.95858	2.95999	1.4226𝑒−03	1.049𝑒−06
0.60	3.56000	3.55858	3.55988	1.4211𝑒−03	1.114𝑒−04
0.80	4.24000	4.23867	4.23924	1.3308𝑒−03	7.522𝑒−04
1.00	5.00000	4.99885	4.99691	1.1485𝑒−03	3.089𝑒−03
𝑛=15,𝜙5
0.00	2.00000	1.99884	2.00000	1.1567𝑒−03	0.000𝑒+00
0.20	2.44000	2.43866	2.44000	1.3394𝑒−03	6.597𝑒−08
0.40	2.96000	2.95857	2.96000	1.4289𝑒−03	2.671𝑒−07
0.60	3.56000	3.55857	3.56000	1.4288𝑒−03	6.143𝑒−07
0.80	4.24000	4.23866	4.24000	1.3394𝑒−03	1.940𝑒−06
1.00	5.00000	4.99884	5.00000	1.1567𝑒−03	1.380𝑒−06