Table 1 Summary of comparison results between the ODE-based method and finite difference scheme. The total number of cells, cell size, the error Er, x̄, and ξ̄ by the finite difference scheme are presented. With the ODE-based method, we have \(\bar{x} = 59.392\) and \(\bar{\xi } = 19.262\)
Total number of cells | Cell size h | Er | x̄ | ξ̄ |
|---|---|---|---|---|
100 | 1.000 | 1.252E−02 | 58.500 | 18.500 |
200 | 0.500 | 8.924E−03 | 59.250 | 19.250 |
300 | 0.333 | 7.301E−03 | 59.167 | 19.167 |
400 | 0.250 | 6.327E−03 | 59.375 | 19.375 |
500 | 0.200 | 5.661E−03 | 59.300 | 19.100 |
600 | 0.167 | 5.170E−03 | 59.250 | 19.083 |
700 | 0.143 | 4.787E−03 | 59.357 | 19.214 |
800 | 0.125 | 4.478E−03 | 59.313 | 19.188 |
900 | 0.111 | 4.222E−03 | 59.389 | 19.278 |
1000 | 0.100 | 4.006E−03 | 59.350 | 19.250 |
1500 | 0.067 | 3.271E−03 | 59.367 | 19.233 |
2000 | 0.050 | 2.833E−03 | 59.375 | 19.275 |
3000 | 0.033 | 2.313E−03 | 59.383 | 19.250 |