Application of Lane-Emden differential equation numerical method in fair value analysis of financial accounting
and | Dec 30, 2021
About this article
Published Online: Dec 30, 2021
Page range: 669 - 676
Received: Jun 17, 2021
Accepted: Sep 24, 2021
DOI: https://doi.org/10.2478/amns.2021.1.00094
Keywords
© 2021 Linying Xu et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.
L∞ error under different parameters
| k | M=3 | M=4 | M=5 | M=6 | M=7 | M=8 |
|---|---|---|---|---|---|---|
| 2 | 2.69e−5 | 1.05e−6 | 5.27e−7 | 1.13e−8 | 8.59e−9 | 2.01e−10 |
| 3 | 1.76e−6 | 6.99e−8 | 7.55e−9 | 4.89e−10 | 2.63e−11 | 1.61e−12 |
L∞ and L2 errors under different parameters
| Haar | Euler | Haar | Euler |
|---|---|---|---|
| k=21.97e−3 | 1.05e−6 | 4.71e−4 | 2.28e−7 |
| k=34.91e−4 | 6.99e−8 | 1.65e−4 | 1.97e −8 |
| k=41.23e−4 | 6.41e−9 | 5.84e−5 | 2.79e −9 |
| k=53.12e−5 | 4.32e−10 | 2.06e−5 | 2.72e −10 |
| k=68.92e−6 | 2.75e−11 | 7.28e−6 | 2.46e −10 |
| k=72.96e−6 | 1.73e−12 | 2.56e−6 | 2.19e −11 |
| k=81.29e−7 | 1.08e−13 | 8.81e−7 | 1.93e −12 |
Comparison of L∞ and L2 errors under different parameters
| L∞ | L∞ | |||
|---|---|---|---|---|
| k=1 | Haar | Euler | Haar | Euler |
| k=2 | 7.80e−4 | 5.36e−5 | 1.63e−3 | 1.68e−4 |
| k=3 | 1.94e −4 | 3.97e−6 | 5.74e−4 | 1.21e −5 |
| k=4 | 4.84e −5 | 2.73e−7 | 2.03e−4 | 8.57e −7 |
| k=5 | 1.21e −5 | 1.76e−8 | 7.18e−5 | 5.50e −8 |
| k=6 | 3.02e −6 | 1.17e−9 | 2.54e−5 | 3.66e −9 |
| k=7 | 7.55e −7 | 7.39e−11 | 8.97e−6 | 2.32e −10 |
| k=8 | 1.89e −7 | 4.59e−12 | 3.17e−6 | 1.44e −11 |
Comparison of numerical solutions and exact solutions with different parameters
| 0 | 0.693147180559945 | 0.693147180559945 | 0.693147180559945 | 0.693147180559945 | |
| 0.1 | 0.683196849706777 | 0.683227245796262 | 0.683197075022063 | 0.683196849437443 | |
| 0.2 | 0.653926467406664 | 0.653969148173502 | 0.653926783980363 | 0.653926466991036 | |
| 0.3 | 0.606969484318893 | 0.607019006611345 | 0.606969843582379 | 0.606969483813016 | |
| 0.4 | 0.544727175441672 | 0.544780344557389 | 0.544727529512898 | 0.544727174911210 | |
| 0.5 | 0.470003629245736 | 0.470056791556372 | 0.470003963513028 | 0.470003628756537 | |
| 0.6 | 0.385662480811985 | 0.385704191793314 | 0.385662747357822 | 0.385662480415734 | |
| 0.7 | 0.294371060602578 | 0.294402255148925 | 0.294371256591398 | 0.294371060311363 | |
| 0.8 | 0.198450938723838 | 0.198471255975016 | 0.198451064512775 | 0.198450938537864 | |
| 0.9 | 0.099820335282211 | 0.099829667365162 | 0.099820397248811 | 0.099820335194224 | |
| 1.0 | 0 | 0 | 0 | 0 | |