Bezier Curves Method for Fourth-Order Integrodifferential Equations

Table 1

Legendre polynomials, presented method, exact, and absolute error of 𝑦(𝑡) for Example 3.

t	Legendre polynomials	Presented method	Exact	Absolute error
0.0	0.0000080	0.00000000000	0.00000000000	0.0
0.1	0.0419474	0.04195072854	0.04195072872	1.773458002×10^−10
0.2	0.0793162	0.07931714637	0.07931714637	2.0180492×10^−12
0.3	0.1124756	0.1124732287	0.1124732286	6.880859813×10^−11
0.4	0.1417531	0.1417508127	0.1417508127	1.025976216×10^−11
0.5	0.1674426	0.1674429185	0.1417508127	1.12222848×10^−11
0.6	0.1898041	0.1898066812	0.1898066813	6.434997580×10^−11
0.7	0.2090640	0.2090659248	0.2090659250	2.239963759×10^−10
0.8	0.2254149	0.2254134028	0.2254134028	2.503659231×10^−11
0.9	0.2390158	0.2390127258	0.2390127256	2.308402409×10^−10
1.0	0.2499920	0.2500000000	0.2500000000	0.0