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 2

The errors and the a posterior error estimate of 𝑥(𝑠) in Example 6.1 at mesh point (ℎ=1/20, 𝛼=−1/2 in combination coefficient).

s	𝐸𝑇	𝐸𝑀	𝐸𝐶	|𝑥(𝑠𝑖)−(𝑇𝑥𝑖+𝑀𝑥𝑖)/2|	|(𝑇𝑥𝑖−𝑀𝑥𝑖)/2|
0.1	−1.526E−03	4.376E−04	−7.358E−06	5.444E−04	9.820E−04
0.2	−1.560E−03	4.709E−04	1.082E−05	5.446E−04	1.016E−03
0.3	−1.557E−03	4.786E−04	1.750E−05	5.391E−04	1.018E−03
0.4	−1.576E−03	4.871E−04	1.963E−05	5.446E−04	1.032E−03
0.5	−1.625E−03	5.013E−04	1.957E−05	5.620E−04	1.063E−03
0.6	−1.705E−03	5.228E−04	1.821E−05	5.909E−04	1.114E−03
0.7	−1.815E−03	5.522E−04	1.596E−05	6.314E−04	1.184E−03
0.8	−1.958E−03	5.901E−04	1.297E−05	6.837E−04	1.274E−03
0.9	−2.135E−03	6.373E−04	9.312E−06	7.487E−04	1.386E−03
1.0	−2.350E−03	6.948E−04	4.944E−06	8.278E−04	1.523E−03
Maximum error	2.350E−03	6.948E−04	1.963E−05	8.278E−04	1.523E−03
Maximum error ratios	2.937	2.908	7.162	2.950	2.931