Application of B-theory for Numerical Method of Functional Differential Equations in the Analysis of Fair Value in Financial Accounting

2020 ◽  
Vol 29 (3) ◽  
Author(s):  
Hengying Dong
Keyword(s):  
Differential Equations ◽  
Numerical Method ◽  
Functional Differential Equations ◽  
Fair Value ◽  
Financial Accounting ◽  
Functional Differential

scholarly journals Financial Accounting Measurement Model Based on Numerical Analysis of Rigid Normal Differential Equation and Rigid Functional Equation

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Zhihua Yan ◽  
Bahjat Fakieh ◽  
Ragab Ibrahim Ismail
Keyword(s):  
Differential Equation ◽  
Functional Equation ◽  
Numerical Analysis ◽  
Functional Differential Equations ◽  
Fair Value ◽  
Measurement Model ◽  
Financial Accounting ◽  
Accounting Measurement ◽  
Functional Differential ◽  
The Stability

Abstract The initial value problem of stiff functional differential equations often appears in many fields such as automatic control, economics and its theoretical and algorithmic research is of unquestionable importance. The paper proposes a rigid functional equation based on the integral process method of the financial accounting measurement model of numerical analysis. This method provides a unified theoretical basis for the stability analysis of the solution of the functional differential equation encountered in the integrodifferential equation and the financial accounting fair value measurement model of investment real estate.

Numerical Analysis of Fractional Neutral Functional Differential Equations Based on Generalized Volterra-Integral Operators

2017 ◽  
Vol 12 (3) ◽  
Author(s):  
Xiao-Li Ding ◽  
Juan J. Nieto
Keyword(s):  
Differential Equation ◽  
Integral Operator ◽  
Differential Equations ◽  
Numerical Method ◽  
Functional Differential Equation ◽  
Functional Differential Equations ◽  
Waveform Relaxation ◽  
Neutral Functional Differential Equation ◽  
Neutral Functional Differential Equations ◽  
Functional Differential

We use waveform relaxation (WR) method to solve numerically fractional neutral functional differential equations and mainly consider the convergence of the numerical method with the help of a generalized Volterra-integral operator associated with the Mittag–Leffler function. We first give some properties of the integral operator. Using the proposed properties, we establish the convergence condition of the numerical method. Finally, we provide a new way to prove the convergence of waveform relaxation method for integer-order neutral functional differential equation, which is a special case of fractional neutral functional differential equation. Compared to the existing proof in the literature, our proof is concise and original.

Numerical Method of Hybrid Stochastic Functional Differential Equations with the Local Lipschitz Coefficients

2011 ◽  
Vol 267 ◽  
pp. 422-426
Author(s):  
Hua Yang ◽  
Feng Jiang ◽  
Jun Hao Hu
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Numerical Method ◽  
Lipschitz Condition ◽  
Numerical Solutions ◽  
Functional Differential Equations ◽  
Stochastic Functional Differential Equations ◽  
Local Lipschitz Condition ◽  
Functional Differential ◽  
Stochastic Functional

Recently, hybrid stochastic differential equations have received a great deal of attention. It is surprising that there are not any numerical schemes established for the hybrid stochastic functional differential equations. In this paper, the Euler—Maruyama method is developed, and the main aim is to show that the numerical solutions will converge to the true solutions under the local Lipschitz condition. The result obtained generalizes the earlier results.

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

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Cheng Chen ◽  
Abdullah Albarakati ◽  
Yuhan Hu
Keyword(s):  
Differential Equations ◽  
Function Analysis ◽  
Functional Differential Equations ◽  
Fair Value ◽  
Measurement Model ◽  
Dominant Mode ◽  
Financial Accounting ◽  
Stability And Convergence ◽  
Fair Value Accounting ◽  
Historical Cost

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.

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