<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>Financial accounting, the use of historical cost of assets, is an important basic principle of historical cost, which is to become the dominant mode of accounting measurement. Background analyses, as well as the historical cost basis and fair value, result from the development of the theory of historical cost and fair value. Historical cost and fair value measurement model has its own advantages and problems. Based on this background, the paper applies B-theoretical numerical methods to differential equations pan function analysis for calculation of fair value accounting and conducts theoretical analysis of their stability and convergence. Finally, numerical examples with different methods of calculating an approximate solution are provided and a comparison of the various methods is done based on the results obtained. The results show fair value accounting better meets the needs of the target –decision-making availability, compared to historical cost or fair value, more in line with the requirements of Accounting Information Quality.</p>
</abstract>

Financial accounting, the use of historical cost of assets, is an important basic principle of historical cost, which is to become the dominant mode of accounting measurement. Background analyses, as well as the historical cost basis and fair value, result from the development of the theory of historical cost and fair value. Historical cost and fair value measurement model has its own advantages and problems. Based on this background, the paper applies B-theoretical numerical methods to differential equations pan function analysis for calculation of fair value accounting and conducts theoretical analysis of their stability and convergence. Finally, numerical examples with different methods of calculating an approximate solution are provided and a comparison of the various methods is done based on the results obtained. The results show fair value accounting better meets the needs of the target –decision-making availability, compared to historical cost or fair value, more in line with the requirements of Accounting Information Quality.

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

Department of Information Systems, Faculty of Computing and Information Technology

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

Financial accounting, the use of historical cost of assets, is an important basic principle of historical cost, which is to become the dominant mode of...

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

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

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

Published Online: Nov 22, 2021

Page range: 193 - 202

Received: Jun 17, 2021

Accepted: Sep 24, 2021

DOI: https://doi.org/10.2478/amns.2021.2.00052

Keywords
fair value, universal function, differential equation, B-theory, financial accounting

© 2021 Cheng Chen et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

B-theoretical algorithm calculation results

Some values of aj

Some values of a*j

Improved B-theoretical algorithm calculation

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

Published Online: Nov 22, 2021

Page range: 193 - 202

Received: Jun 17, 2021

Accepted: Sep 24, 2021

DOI: https://doi.org/10.2478/amns.2021.2.00052

Keywordsfair value, universal function, differential equation, B-theory, financial accounting

© 2021 Cheng Chen et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

B-theoretical algorithm calculation results

Some values of aj

Some values of a*j

Improved B-theoretical algorithm calculation

Keywords
fair value, universal function, differential equation, B-theory, financial accounting