High Accuracy Combination Method for Solving the Systems of Nonlinear Volterra Integral and Integro-Differential Equations with Weakly Singular Kernels of the Second Kind

Table 1

The errors and the a posterior error estimate of 𝑥(𝑠) in Example 6.1 at mesh point (ℎ=1/10, 𝛼=−1/2 in combination coefficient).

s	𝐸𝑇	𝐸𝑀	𝐸𝐶	|𝑥(𝑠𝑖)−(𝑇𝑥𝑖+𝑀𝑥𝑖)/2|	|(𝑇𝑥𝑖−𝑀𝑥𝑖)/2|
0.1	−3.871E−03	9.519E−04	−1.406E−04	1.459E−03	2.411E−03
0.2	−4.559E−03	1.313E−03	−1.764E−05	1.623E−03	2.936E−03
0.3	−4.664E−03	1.381E−03	1.129E−05	1.642E−03	3.022E−03
0.4	−4.758E−03	1.428E−03	2.692E−05	1.665E−03	3.093E−03
0.5	−4.908E−03	1.480E−03	3.323E−05	1.714E−03	3.194E−03
0.6	−5.130E−03	1.546E−03	3.369E−05	1.792E−03	3.338E−03
0.7	−5.434E−03	1.630E−03	2.996E−05	1.902E−03	3.532E−03
0.8	−5.824E−03	1.735E−03	2.281E−05	2.044E−03	3.779E−03
0.9	−6.310E−03	1.864E−03	1.249E−05	2.223E−03	4.087E−03
1.0	−6.904E−03	2.021E−03	−1.165E−06	2.442E−03	4.462E−03
Maximum error	6.904E−03	2.021E−03	1.406E−04	2.442E−03	4.462E−03