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A peer-reviewed article of this preprint also exists.
This version is not peer-reviewed
Exact solution |
AGM Eq. (12) |
Error% | Exact solution |
AGM Eq. (12) |
Error% | Exact solution |
AGM Eq. (12) |
Error% | |
0 | 0.0522 | 0.0527 | 0.9578 | 0.1733 | 0.1795 | 3.5776 | 0.3290 | 0.3474 | 5.5927 |
0.2 | 0.0501 | 0.0505 | 0.7984 | 0.1661 | 0.1689 | 1.6857 | 0.3148 | 0.3246 | 3.1131 |
0.4 | 0.0436 | 0.0439 | 0.6881 | 0.1443 | 0.1440 | 0.2079 | 0.2728 | 0.2768 | 1.4663 |
0.6 | 0.0329 | 0.0330 | 0.3039 | 0.1085 | 0.1087 | 0.1843 | 0.2040 | 0.2060 | 0.9804 |
0.8 | 0.0180 | 0.0180 | 0.0000 | 0.0590 | 0.0590 | 0.0000 | 0.1102 | 0.1102 | 0.0000 |
1 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |
Average error (%) | 0.4580 | Average error (%) | 0.9426 | Average error (%) | 1.8587 |
Num. | AGM Eq. (12). This work |
HAM [11] Eq. (14) |
PM [10] Eq. (15) |
Error % AGM Eq. (12) This work |
Error % HAM [11] Eq. (14) |
Error % PM [10] Eq. (15) |
|
0 | 0.0517 | 0.0517 | 0.0517 | 0.0516 | 0.0000 | 0.0000 | 0.1934 |
0.2 | 0.0496 | 0.0496 | 0.0496 | 0.0495 | 0.0000 | 0.0000 | 0.2016 |
0.4 | 0.0432 | 0.0436 | 0.0434 | 0.0433 | 0.9259 | 0.0230 | 0.4629 |
0.6 | 0.0327 | 0.0324 | 0.0330 | 0.0329 | 0.9174 | 0.0303 | 0.6116 |
0.8 | 0.0179 | 0.0180 | 0.0185 | 0.0185 | 0.5586 | 3.3519 | 3.3519 |
1 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |
Average error (%) | 0.3493 | 0.5675 | 0.8036 |
Num. | AGM Eq. (12). This work |
HAM [11] Eq. (14) |
PM [10] Eq. (15) |
Error % AGM Eq. (12) This work |
Error % HAM [11] Eq. (14) |
Error % PM [10] Eq. (15) |
||
0 | 0.3045 | 0.3201 | 0.2951 | 0.2823 | 4.8133 | 3.0870 | 7.2906 | |
0.2 | 0.2916 | 0.3001 | 0.2829 | 0.2707 | 2.8000 | 2.9835 | 7.1673 | |
0.4 | 0.2532 | 0.2548 | 0.2466 | 0.2363 | 0.6319 | 2.5671 | 6.6745 | |
0.6 | 0.1899 | 0.1893 | 0.1869 | 0.1792 | 0.3159 | 1.5798 | 5.6334 | |
0.8 | 0.1031 | 0.1030 | 0.1041 | 0.1002 | 0.0970 | 0.9699 | 2.8128 | |
1 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | |
Average error (%) | 1.4430 | 1.8645 | 4.9298 |
Num. | AGM Eq. (12). This work |
HAM [11] Eq. (14) |
PM [10] Eq. (16) |
Error % AGM Eq. (12) This work |
Error % HAM [11] Eq. (14) |
Error % PM [10] Eq. (16) |
||
0 | 0.0522 | 0.0523 | 0.0521 | 0.0522 | 0.1916 | 0.1916 | 0.0000 | |
0.2 | 0.0501 | 0.0501 | 0.0500 | 0.0501 | 0.0000 | 0.1996 | 0.0000 | |
0.4 | 0.0436 | 0.0437 | 0.0437 | 0.0438 | 0.2294 | 0.2294 | 0.4587 | |
0.6 | 0.0329 | 0.0331 | 0.0332 | 0.0333 | 0.6079 | 0.9118 | 1.2158 | |
0.8 | 0.0180 | 0.0181 | 0.0188 | 0.0187 | 0.5555 | 4.4444 | 3.8889 | |
1 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | |
Average error (%) | 0.2641 | 0.9961 | 0.9272 |
Num. | AGM Eq. (12). This work |
HAM [11] Eq. (14) |
PM [10] Eq. (16) |
Error % AGM Eq. (12) This work |
Error % HAM [11] Eq. (14) |
Error % PM [10] Eq. (16) |
|
0 | 0.3255 | 0.3208 | 0.3192 | 0.3172 | 1.4439 | 1.9355 | 2.5499 |
0.2 | 0.3116 | 0.3077 | 0.3059 | 0.3040 | 1.2516 | 1.8292 | 2.4390 |
0.4 | 0.2701 | 0.2684 | 0.2662 | 0.2646 | 0.6294 | 1.4439 | 2.0363 |
0.6 | 0.2021 | 0.2030 | 0.2011 | 0.1994 | 0.4433 | 0.4948 | 1.3360 |
0.8 | 0.1093 | 0.1113 | 0.1117 | 0.1110 | 1.8230 | 2.1958 | 1.5553 |
1 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |
Average error (%) | 0.9319 | 1.3163 | 1.6527 |
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
Submitted:
05 July 2023
Posted:
21 July 2023
You are already at the latest version
A peer-reviewed article of this preprint also exists.
This version is not peer-reviewed
Submitted:
05 July 2023
Posted:
21 July 2023
You are already at the latest version
Exact solution |
AGM Eq. (12) |
Error% | Exact solution |
AGM Eq. (12) |
Error% | Exact solution |
AGM Eq. (12) |
Error% | |
0 | 0.0522 | 0.0527 | 0.9578 | 0.1733 | 0.1795 | 3.5776 | 0.3290 | 0.3474 | 5.5927 |
0.2 | 0.0501 | 0.0505 | 0.7984 | 0.1661 | 0.1689 | 1.6857 | 0.3148 | 0.3246 | 3.1131 |
0.4 | 0.0436 | 0.0439 | 0.6881 | 0.1443 | 0.1440 | 0.2079 | 0.2728 | 0.2768 | 1.4663 |
0.6 | 0.0329 | 0.0330 | 0.3039 | 0.1085 | 0.1087 | 0.1843 | 0.2040 | 0.2060 | 0.9804 |
0.8 | 0.0180 | 0.0180 | 0.0000 | 0.0590 | 0.0590 | 0.0000 | 0.1102 | 0.1102 | 0.0000 |
1 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |
Average error (%) | 0.4580 | Average error (%) | 0.9426 | Average error (%) | 1.8587 |
Num. | AGM Eq. (12). This work |
HAM [11] Eq. (14) |
PM [10] Eq. (15) |
Error % AGM Eq. (12) This work |
Error % HAM [11] Eq. (14) |
Error % PM [10] Eq. (15) |
|
0 | 0.0517 | 0.0517 | 0.0517 | 0.0516 | 0.0000 | 0.0000 | 0.1934 |
0.2 | 0.0496 | 0.0496 | 0.0496 | 0.0495 | 0.0000 | 0.0000 | 0.2016 |
0.4 | 0.0432 | 0.0436 | 0.0434 | 0.0433 | 0.9259 | 0.0230 | 0.4629 |
0.6 | 0.0327 | 0.0324 | 0.0330 | 0.0329 | 0.9174 | 0.0303 | 0.6116 |
0.8 | 0.0179 | 0.0180 | 0.0185 | 0.0185 | 0.5586 | 3.3519 | 3.3519 |
1 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |
Average error (%) | 0.3493 | 0.5675 | 0.8036 |
Num. | AGM Eq. (12). This work |
HAM [11] Eq. (14) |
PM [10] Eq. (15) |
Error % AGM Eq. (12) This work |
Error % HAM [11] Eq. (14) |
Error % PM [10] Eq. (15) |
||
0 | 0.3045 | 0.3201 | 0.2951 | 0.2823 | 4.8133 | 3.0870 | 7.2906 | |
0.2 | 0.2916 | 0.3001 | 0.2829 | 0.2707 | 2.8000 | 2.9835 | 7.1673 | |
0.4 | 0.2532 | 0.2548 | 0.2466 | 0.2363 | 0.6319 | 2.5671 | 6.6745 | |
0.6 | 0.1899 | 0.1893 | 0.1869 | 0.1792 | 0.3159 | 1.5798 | 5.6334 | |
0.8 | 0.1031 | 0.1030 | 0.1041 | 0.1002 | 0.0970 | 0.9699 | 2.8128 | |
1 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | |
Average error (%) | 1.4430 | 1.8645 | 4.9298 |
Num. | AGM Eq. (12). This work |
HAM [11] Eq. (14) |
PM [10] Eq. (16) |
Error % AGM Eq. (12) This work |
Error % HAM [11] Eq. (14) |
Error % PM [10] Eq. (16) |
||
0 | 0.0522 | 0.0523 | 0.0521 | 0.0522 | 0.1916 | 0.1916 | 0.0000 | |
0.2 | 0.0501 | 0.0501 | 0.0500 | 0.0501 | 0.0000 | 0.1996 | 0.0000 | |
0.4 | 0.0436 | 0.0437 | 0.0437 | 0.0438 | 0.2294 | 0.2294 | 0.4587 | |
0.6 | 0.0329 | 0.0331 | 0.0332 | 0.0333 | 0.6079 | 0.9118 | 1.2158 | |
0.8 | 0.0180 | 0.0181 | 0.0188 | 0.0187 | 0.5555 | 4.4444 | 3.8889 | |
1 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | |
Average error (%) | 0.2641 | 0.9961 | 0.9272 |
Num. | AGM Eq. (12). This work |
HAM [11] Eq. (14) |
PM [10] Eq. (16) |
Error % AGM Eq. (12) This work |
Error % HAM [11] Eq. (14) |
Error % PM [10] Eq. (16) |
|
0 | 0.3255 | 0.3208 | 0.3192 | 0.3172 | 1.4439 | 1.9355 | 2.5499 |
0.2 | 0.3116 | 0.3077 | 0.3059 | 0.3040 | 1.2516 | 1.8292 | 2.4390 |
0.4 | 0.2701 | 0.2684 | 0.2662 | 0.2646 | 0.6294 | 1.4439 | 2.0363 |
0.6 | 0.2021 | 0.2030 | 0.2011 | 0.1994 | 0.4433 | 0.4948 | 1.3360 |
0.8 | 0.1093 | 0.1113 | 0.1117 | 0.1110 | 1.8230 | 2.1958 | 1.5553 |
1 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |
Average error (%) | 0.9319 | 1.3163 | 1.6527 |
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
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