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 6

The errors and the a posterior error estimate of 𝑥(𝑠), that is, 𝑢(𝑠) in Example 6.2 at mesh point (ℎ=1/20, 𝛼=−3/5 in combination coefficient).

s	𝐸𝑇	𝐸𝑀	𝐸𝐶	|𝑢(𝑠𝑖)−(𝑇𝑢𝑖+𝑀𝑢𝑖)/2|	|(𝑇𝑢𝑖−𝑀𝑢𝑖)/2|
0.1	1.576E−05	−5.207E−06	−1.119E−06	5.279E−06	1.049E−05
0.2	9.596E−05	−2.543E−05	−1.763E−06	3.527E−05	6.069E−05
0.3	2.555E−04	−6.436E−05	−2.019E−06	9.554E−05	1.599E−04
0.4	5.067E−04	−1.252E−04	−2.052E−06	1.907E−04	3.159E−04
0.5	8.701E−04	−2.130E−04	−1.870E−06	3.286E−04	5.416E−04
0.6	1.379E−03	−3.356E−04	−1.398E−06	5.216E−04	8.571E−04
0.7	2.083E−03	−5.049E−04	−4.622E−07	7.890E−04	1.294E−03
0.8	3.060E−03	−7.394E−04	1.267E−06	1.160E−03	1.900E−03
0.9	4.428E−03	−1.067E−03	4.395E−06	1.680E−03	2.747E−03
1.0	6.366E−03	−1.529E−03	1.003E−05	2.419E−03	3.948E−03
Maximum error	6.366E−03	1.529E−03	1.003E−05	2.419E−03	3.948E−03
Maximum error ratio	2.729	2.659	11.307	2.751	2.715