Nonlinear Volterra Integral Equation of the Second Kind and Biorthogonal Systems

Table 1

Absolute errors for Example 4.1.

𝑡𝑖	𝑗=9	𝑗=17	𝑗=33	𝑗=65	𝑗=129
	|𝑧2(𝑡𝑖)−𝑥(𝑡𝑖)|	|𝑧2(𝑡𝑖)−𝑥(𝑡𝑖)|	|𝑧2(𝑡𝑖)−𝑥(𝑡𝑖)|	|𝑧2(𝑡𝑖)−𝑥(𝑡𝑖)|	|𝑧2(𝑡𝑖)−𝑥(𝑡𝑖)|
0.125	3.93𝐸−5	9.71𝐸−6	2.34𝐸−6	5.47𝐸−7	1.17𝐸−7
0.250	1.50𝐸−4	3.51𝐸−5	7.65𝐸−6	1.36𝐸−6	6.74𝐸−8
0.375	3.54𝐸−4	1.01𝐸−4	3.19𝐸−5	1.13𝐸−5	4.52𝐸−6
0.5	8.61𝐸−4	2.91𝐸−4	1.11𝐸−4	4.73𝐸−5	2.16𝐸−5
0.625	8.77𝐸−4	2.73𝐸−4	9.66𝐸−5	3.85𝐸−5	1.68𝐸−5
0.750	1.39𝐸−3	4.86𝐸−4	1.92𝐸−4	8.38𝐸−5	3.89𝐸−5
0.875	1.35𝐸−3	4.31𝐸−4	1.54𝐸−4	6.26𝐸−5	2.77𝐸−5
1	2.76𝐸−3	1.04𝐸−3	4.40𝐸−4	2.00𝐸−4	9.51𝐸−5