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.

scholarly journals Financial accounting measurement model based on numerical analysis of rigid normal differential equation and rigid generalised functional equation

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Qiuhong Liu ◽  
Bo Dai ◽  
Iyad Katib ◽  
Mohammed Alaa Alhamami
Keyword(s):  
Differential Equation ◽  
Functional Equation ◽  
Numerical Analysis ◽  
Mathematical Knowledge ◽  
Measurement Model ◽  
Financial Accounting ◽  
Model Based ◽  
Accounting Measurement ◽  
Accounting Environment

Abstract In order to solve the problems of financial accounting measurement quickly and accurately, this paper starts the analysis from the perspective of mathematics and finance and establishes the differential equation and the generalised functional equation for the related numerical analysis through mathematical knowledge. The results show that the limit and integral of rigid differential equation and the rigid generalised functional equation can improve their role and status in the financial accounting measurement environment so that they can be more widely used in the financial accounting measurement environment and promote the development of the financial accounting environment.

On the generalized pantograph functional-differential equation

1993 ◽  
Vol 4 (1) ◽  
pp. 1-38 ◽  
Author(s):  
A. Iserles
Keyword(s):  
Differential Equation ◽  
Stability Boundary ◽  
Functional Differential Equations ◽  
Well Posedness ◽  
Almost Periodic ◽  
Pantograph Equation ◽  
Special Cases ◽  
Rotationally Symmetric ◽  
Functional Differential ◽  
The Stability

The generalized pantograph equation y′(t) = Ay(t) + By(qt) + Cy′(qt), y(0) = y0, where q ∈ (0, 1), has numerous applications, as well as being a useful paradigm for more general functional-differential equations with monotone delay. Although many special cases have been already investigated extensively, a general theory for this equation is lacking–its development and exposition is the purpose of the present paper. After deducing conditions on A, B, C ∈ ℂd×d that are equivalent to well-posedness, we investigate the expansion of y in Dirichlet series. This provides a very fruitful form for the investigation of asymptotic behaviour, and we duly derive conditions for limt⋅→∞y(t) = 0. The behaviour on the stability boundary possesses no comprehensive explanation, but we are able to prove that, along an important portion of that boundary, y is almost periodic and, provided that q is rational, it is almost rotationally symmetric. The paper also addresses itself to a detailed analysis of the scalar equation y′(t) = by(qt), y(0) = 1, to high-order pantograph equations, to a phenomenon, similar to resonance, that occurs for specific configurations of eigenvalues of A, and to the equation Y′(t) = AY(t) + Y(qt) B, Y(0) = Y0.

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.

scholarly journals Periodic Perturbations of a Class of Functional Differential Equations

2021 ◽  
Author(s):  
Marco Spadini
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Functional Equation ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Functional Differential Equations ◽  
Bounded Solutions ◽  
Differentiable Manifolds ◽  
Periodic Perturbations ◽  
Functional Differential

AbstractWe study the existence of a connected “branch” of periodic solutions of T-periodic perturbations of a particular class of functional differential equations on differentiable manifolds. Our result is obtained by a combination of degree-theoretic methods and a technique that allows to associate the bounded solutions of the functional equation to bounded solutions of a suitable ordinary differential equation.

scholarly journals Analytic Solutions of an Iterative Functional Differential Equations Near Regular Points

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Lingxia Liu
Keyword(s):  
Differential Equation ◽  
Functional Equation ◽  
Differential Equations ◽  
Existence Theorem ◽  
Unknown Function ◽  
Functional Differential Equations ◽  
Analytic Solutions ◽  
Functional Differential ◽  
Iterative Functional Differential Equation ◽  
The Given

The existence of analytic solutions of an iterative functional differential equation is studied when the given functions are all analytic and when the given functions have regular points. By reducing the equation to another functional equation without iteration of the unknown function an existence theorem is established for analytic solutions of the original equation.

Branching processes and functional differential equations determining steady-size distributions in cell populations

1995 ◽  
Vol 32 (01) ◽  
pp. 1-10
Author(s):  
Ziad Taib
Keyword(s):  
Differential Equation ◽  
Branching Process ◽  
Branching Processes ◽  
Functional Differential Equations ◽  
Cell Populations ◽  
Size Distributions ◽  
Multitype Branching Process ◽  
Functional Differential ◽  
Intuitive Interpretation ◽  
Infinite Sum

The functional differential equation y′(x) = ay(λx) + by(x) arises in many different situations. The purpose of this note is to show how it arises in some multitype branching process cell population models. We also show how its solution can be given an intuitive interpretation as the probability density function of an infinite sum of independent but not identically distributed random variables.

scholarly journals Bifurcation Analysis in a Diffusive Mussel-Algae Model with Delay

2019 ◽  
Vol 29 (11) ◽  
pp. 1950144 ◽  
Author(s):  
Zuolin Shen ◽  
Junjie Wei
Keyword(s):  
Hopf Bifurcation ◽  
Functional Differential Equations ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Delayed Reaction ◽  
Center Manifold Reduction ◽  
Existence Of Positive Solutions ◽  
Boundary Equilibrium ◽  
Functional Differential ◽  
The Stability

In this paper, we consider the dynamics of a delayed reaction–diffusion mussel-algae system subject to Neumann boundary conditions. When the delay is zero, we show the existence of positive solutions and the global stability of the boundary equilibrium. When the delay is not zero, we obtain the stability of the positive constant steady state and the existence of Hopf bifurcation by analyzing the distribution of characteristic values. By using the theory of normal form and center manifold reduction for partial functional differential equations, we derive an algorithm that determines the direction of Hopf bifurcation and the stability of bifurcating periodic solutions. Finally, some numerical simulations are carried out to support our theoretical results.

On the stability of invariant sets of functional differential equations

2003 ◽  
Vol 55 (6) ◽  
pp. 641-656 ◽  
Author(s):  
Stephen R. Bernfeld ◽  
Constantin Corduneanu ◽  
Alexander O. Ignatyev
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Invariant Sets ◽  
Functional Differential ◽  
The Stability
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