On Bernstein Polynomials Method to the System of Abel Integral Equations

Table 1

Numerical results for Example 2.

𝑠𝑖=0.1𝑖	Exact solution		Proposed method		TEM
	𝜑1(𝑠𝑖)	𝜑2(𝑠𝑖)	𝜑1,5(𝑠𝑖)	𝜑2,5(𝑠𝑖)	𝜑1,5(𝑠𝑖)	𝜑2,5(𝑠𝑖)
𝑖=1	0.2153	1.1072	0.215290	1.107242	0.215169	1.107682
𝑖=2	0.3259	0.8541	0.325884	0.854115	0.325780	0.854328
𝑖=3	0.4276	0.7555	0.427565	0.755497	0.427509	0.755881
𝑖=4	0.5293	0.7046	0.529335	0.704608	0.529611	0.704209
𝑖=5	0.6350	0.6752	0.635031	0.675237	0.635295	0.675831
𝑖=6	0.7470	0.6575	0.747040	0.657498	0.747548	0.657637
𝑖=7	0.8672	0.6468	0.867187	0.646770	0.867735	0.646340
𝑖=8	0.9971	0.6406	0.997089	0.640586	0.997818	0.640385
𝑖=9	1.1383	0.6375	1.138298	0.637503	1.138803	0.637804
𝑖=10	1.2924	0.6366	1.292388	0.636619	1.292765	0.636391