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Application of B-theory for numerical method of functional differential equations in the analysis of fair value in financial accounting

Cheng Chen

Cheng Chen

Business School, Xinyang Vocational and Technical CollegeXinyang, China
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Chen, Cheng
, 
Abdullah Albarakati

Abdullah Albarakati

Department of Information Systems, Faculty of Computing and Information Technology, King Abdulaziz UniversityJeddah, Saudi Arabia
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Albarakati, Abdullah
 und 
Yuhan Hu

Yuhan Hu

Business School, Xinyang Vocational and Technical CollegeXinyang, China
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Hu, Yuhan
  
22. Nov. 2021
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Online veröffentlicht: 22. Nov. 2021
Seitenbereich: 193 - 202
Eingereicht: 17. Juni 2021
Akzeptiert: 24. Sept. 2021
DOI: https://doi.org/10.2478/amns.2021.2.00052
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© 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.
B-theoretical image representation.

Fig. 2

Ladder formula.
Ladder formula.

Fig. 3

Runge-Kutta method.
Runge-Kutta method.

Fig. 4

Adams extrapolation.
Adams extrapolation.

Fig. 5

Adams interpolation.
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
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