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 5

The errors and the a posterior error estimate of 𝑥(𝑠), that is, 𝑢(𝑠) in Example 6.2 at mesh point (ℎ=1/10, 𝛼=−3/5 in combination coefficient).

s	𝐸𝑇	𝐸𝑀	𝐸𝐶	|𝑢(𝑠𝑖)−(𝑇𝑢𝑖+𝑀𝑢𝑖)/2|	|(𝑇𝑢𝑖−𝑀𝑢𝑖)/2|
0.1	5.977E−05	−1.630E−05	−1.470E−06	2.174E−05	3.804E−05
0.2	2.767E−04	−7.095E−05	−3.177E−06	1.029E−04	1.738E−04
0.3	7.027E−04	−1.738E−04	−2.926E−06	2.645E−04	4.382E−04
0.4	1.374E−03	−3.342E−04	−1.214E−06	5.199E−04	8.541E−04
0.5	2.348E−03	−5.659E−04	2.229E−06	8.912E−04	1.457E−03
0.6	3.717E−03	−8.898E−04	8.219E−06	1.414E−03	2.303E−03
0.7	5.621E−03	−1.338E−03	1.830E−05	2.141E−03	3.480E−03
0.8	8.278E−03	−1.961E−03	3.525E−05	3.159E−03	5.119E−03
0.9	1.202E−02	−2.832E−03	6.397E−05	4.595E−03	7.427E−03
1.0	1.737E−02	−4.066E−03	1.134E−04	6.653E−03	1.072E−02
Maximum error	1.737E−02	4.066E−03	1.134E−04	6.653E−03	1.072E−02