Solving the Economic Growth Acceleration Model with Memory Effects: An Application of Combined Theorem of Adomian Decomposition Methods and Kashuri–Fundo Transformation Methods

The primary purpose of this study is to solve the economic growth acceleration model with memory effects for the quadratic cost function (Riccati fractional differential equation), using Combined Theorem of Adomian Polynomial Decomposition and Kashuri–Fundo Transformation methods. The economic growt...

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Bibliographic Details
Published in:Symmetry (Basel) 2022-01, Vol.14 (2), p.192
Main Authors: Johansyah, Muhamad Deni, Supriatna, Asep K., Rusyaman, Endang, Saputra, Jumadil
Format: Article
Language:English
Subjects:
adomian decomposition method
Calculus
combined theorem
Cost analysis
Cost function
Costs
Decomposition
Differential equations
Economic development
Economic growth
economic growth model
Economic models
Exact solutions
Fourier transforms
GDP
Gross Domestic Product
Growth models
Kashuri–Fundo transformation
Mathematical models
Polynomials
Production increases
riccati fractional differential equation
Theorems
Transformations (mathematics)
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Summary:The primary purpose of this study is to solve the economic growth acceleration model with memory effects for the quadratic cost function (Riccati fractional differential equation), using Combined Theorem of Adomian Polynomial Decomposition and Kashuri–Fundo Transformation methods. The economic growth model (EGM) with memory effects for the quadratic cost function is analysed by modifying the linear fractional differential equation. The study’s significant contribution is to develop a linear cost function in the EGM for a quadratic non-linear cost function and determine the specific conditions of the Riccati fractional differential equation (RFDEs) in the EGM with memory effects. The study results showed that RFDEs in the EGM involving the memory effect have a solution and singularity. Additionally, this study presents a comparison of exact solutions using Lie symmetry, Combined Theorem of Adomian Polynomial Decomposition, and Kashuri–Fundo Transformation methods. The results showed that the three methods have the same solution. Furthermore, this study provides a numerical solution to the RFDEs on the EGM with memory effects. The numerical simulation results showed that the output value of Y(t) for the quadratic cost function in the economic growth model is significantly affected by the memory effect.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym14020192