Application of B-theory for numerical method of functional differential equations in the analysis of fair value in financial accounting
Publié en ligne: 22 nov. 2021
Pages: 193 - 202
Reçu: 17 juin 2021
Accepté: 24 sept. 2021
© 2021 Cheng Chen et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.
Fig. 1
B-theoretical image representation.Fig. 2
Ladder formula.Fig. 3
Runge-Kutta method.Fig. 4
Adams extrapolation.Fig. 5
Adams interpolation.B-theoretical algorithm calculation results
x[i] points |
y[i] (numerical solution) |
y(x[i]) (exact solution) |
|y(x[i]) − y[i]| (error) |
|
0.1 |
1.000000 |
0.990099 |
0.009901 |
0.2 |
0.980000 |
0.961538 |
0.018462 |
0.3 |
0.941584 |
0.917431 |
0.024153 |
0.4 |
0.888389 |
0.862069 |
0.026320 |
0.5 |
0.825250 |
0.800000 |
0.025250 |
0.6 |
0.757147 |
0.735294 |
0.021852 |
0.7 |
0.688354 |
0.671141 |
0.017213 |
0.8 |
0.622018 |
0.609756 |
0.012262 |
0.9 |
0.560113 |
0.552486 |
0.007626 |
1.0 |
0.503642 |
0.500000 |
0.003642 |
1.1 |
0.452911 |
0.452489 |
0.000422 |
1.2 |
0.407783 |
0.409836 |
0.002053 |
Some values of aj
j |
0 |
1 |
2 |
3 |
4 |
5 |
··· |
aj |
1 |
1/2 |
5/12 |
3/8 |
251/720 |
95/288 |
⋯ |
Some values of a*j
j |
0 |
1 |
2 |
3 |
4 |
5 |
⋯ |
a*j |
1 |
−1/2 |
−1/12 |
−1/24 |
−19/720 |
−3/160 |
⋯ |
Improved B-theoretical algorithm calculation
x[i] points |
y[i] (numerical solution) |
y(x[i]) (exact solution) |
|y(x[i]) − y[i]| (error) |
|
0.1 |
0.990000 |
0.990099 |
0.000099 |
0.2 |
0.961366 |
0.961538 |
0.000173 |
0.3 |
0.917246 |
0.917431 |
0.000185 |
0.4 |
0.861954 |
0.862069 |
0.000115 |
0.5 |
0.800034 |
0.800000 |
0.000034 |
0.6 |
0.735527 |
0.735294 |
0.000233 |
0.7 |
0.671587 |
0.671141 |
0.000446 |
0.8 |
0.610399 |
0.609756 |
0.000643 |
0.9 |
0.553289 |
0.552486 |
0.000803 |
1.0 |
0.500919 |
0.500000 |
0.000919 |
1.1 |
0.453479 |
0.452489 |
0.000990 |
1.2 |
0.410859 |
0.409836 |
0.001023 |