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 4

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

s	𝐸𝑇	𝐸𝑀	𝐸𝐶	|𝑦(𝑠𝑖)−(𝑇𝑦𝑖+𝑀𝑦𝑖)/2|	|(𝑇𝑦𝑖−𝑀𝑦𝑖)/2|
0.1	1.748E−03	−4.874E−04	1.914E−05	6.305E−04	1.118E−03
0.2	1.298E−03	−3.659E−04	1.110E−05	4.662E−04	8.321E−04
0.3	1.311E−03	−3.680E−04	1.234E−05	4.715E−04	8.396E−04
0.4	1.450E−03	−4.058E−04	1.467E−05	5.222E−04	9.280E−04
0.5	1.657E−03	−4.622E−04	1.778E−05	5.972E−04	1.059E−03
0.6	1.915E−03	−5.328E−04	2.164E−05	6.909E−04	1.224E−03
0.7	2.221E−03	−6.166E−04	2.628E−05	8.023E−04	1.419E−03
0.8	2.579E−03	−7.143E−04	3.179E−05	9.324E−04	1.647E−03
0.9	2.995E−03	−8.277E−04	3.834E−05	1.084E−03	1.912E−03
1.0	3.481E−03	−9.597E−04	4.618E−05	1.260E−03	2.220E−03
Maximum error	3.481E−03	9.597E−04	4.618E−05	1.260E−03	2.220E−03
Maximum error ratios	2.817	2.800	3.137	2.824	2.814