Approximate Solutions of Differential Equations by Using the Bernstein Polynomials

Table 1

Numerical results for Example 7.1.

𝑥	Exact solution	Method of [12]	Method of [13]	Method of [14]	Presented method
		for 𝑁=8	for 𝑁=8	for𝑁=8	for𝑚=8
0	1	1	1	1	0.9999999992
0.1	0.9946538263	0.9946538263	0.9946538262	0.9946538266	0.9946538261
0.2	0.9771222065	0.9771222065	0.9771222014	0.9771222093	0.9771222065
0.3	0.9449011653	0.9449011653	0.9449010769	0.9449011752	0.9449011655
0.4	0.8950948186	0.8950948186	0.8950941522	0.8950948487	0.8950948184
0.5	0.8243606354	0.8243606356	0.8243574386	0.8243607328	0.8243606353
0.6	0.7288475202	0.728847522	0.7288359969	0.7288478604	0.7288475204
0.7	0.6041258122	0.6041258211	0.6040917111	0.6041269662	0.6041258121
0.8	0.4451081857	0.4451082201	0.4450208387	0.4451117669	0.4451081857
0.9	0.2459603111	0.2459604249	0.2457599482	0.2459703618	0.2459603113
1	0	3.326×10^−7	−4.213×10^−4	2.57×10^−5	8×10^−10