Analysis of Reliable Solutions to the Boundary Value Problems by Using Shooting Method

Table 1

Results of consecutive four iterations along with exact solution and error estimation for numerical problem-1.

Xi	Approximate solution				Exact value	Error
	Iteration 1	Iteration 2	Iteration 3	Iteration 4
0.1	−0.2844973	−0.3081503	−0.3081503	−0.3081503	−0.3084846	0.0003343
0.2	−0.2628842	−0.3131762	−0.3131762	−0.3131762	−0.3138869	0.0007107
0.3	−0.2342192	−0.3150113	−0.3150113	−0.3150113	−0.3161530	0.0011417
0.4	−0.1974160	−0.3136180	−0.3136180	−0.3136180	−0.3152601	0.0016421
0.5	−0.1512034	−0.3089876	−0.3089876	−0.3089876	−0.3112173	0.0022297
0.6	−0.0940749	−0.3011389	−0.3011389	−0.3011389	−0.3040649	0.0029260
0.7	−0.0242281	−0.2901171	−0.2901171	−0.2901171	−0.2938744	0.0037572
0.8	0.0605100	−0.2759925	−0.2759925	−0.2759925	−0.2807476	0.0047551
0.9	0.1627746	−0.2588576	−0.2588576	−0.2588576	−0.2648157	0.0059580
1.0	0.2857734	−0.2388248	−0.2388248	−0.2388248	−0.2462378	0.0074130
1.1	0.4334233	−0.2160224	−0.2160224	−0.2160224	−0.2251996	0.0091772
1.2	0.6105155	0.1905909	−0.1905909	−0.1905909	−0.2019112	0.0113203
1.3	0.8229173	−0.1626782	−0.1626782	−0.1626782	−0.1766055	0.0139273
1.4	1.0778193	−0.1324332	−0.1324332	−0.1324332	−0.1495351	0.0171019
1.5	1.3840353	−0.1000000	−0.1000000	−0.1000000	−0.1209707	0.0209707