Modelling of natural growth with memory effect in economics: An application of adomian decomposition and variational iteration methods

The power-law memory effect is taken into consideration in a generalisation of the economic model of natural growth. The memory effect refers to a process's reliance on its current state and its history of previous changes. However, the study that focuses on natural growth in economics...

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Autores principales: Muhamad Deni Johansyah, Asep K. Supriatna, Endang Rusyaman, Jumadil Saputra
Formato: article
Lenguaje:EN
Publicado: Growing Science 2022
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Acceso en línea:https://doaj.org/article/10e954c29a5c4ac798d63c0c9be690c0
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spelling oai:doaj.org-article:10e954c29a5c4ac798d63c0c9be690c02021-11-12T06:26:20ZModelling of natural growth with memory effect in economics: An application of adomian decomposition and variational iteration methods1929-58041929-581210.5267/j.dsl.2021.8.003https://doaj.org/article/10e954c29a5c4ac798d63c0c9be690c02022-01-01T00:00:00Zhttp://www.growingscience.com/dsl/Vol11/dsl_2021_31.pdfhttps://doaj.org/toc/1929-5804https://doaj.org/toc/1929-5812 The power-law memory effect is taken into consideration in a generalisation of the economic model of natural growth. The memory effect refers to a process's reliance on its current state and its history of previous changes. However, the study that focuses on natural growth in economics considering the memory effect with fractional order-linear differential equation model is still limited. The current investigation seeks to solve the natural growth with memory effect in the economics model and decide the best model using fractional differential equation (FDE), namely Adomian Decomposition and Variational Iteration Methods. Also, this study assumes the level of consumer loss memory during a certain time interval denoted by a parameter (α). This study showed the model of loss memory effect with 0 < α ≤ 1 given a slowdown in output growth compared to a model without memory effect. Besides that, this study also found that output Y(t) is growing faster with the Variational Iteration method compared to the Adomian decomposition method. Also, using graphical simulation, this study found the output Y(t) is closer to the exact solution with α=0.4 and α=0.9. In conclusion, this study successfully solved natural growth with memory effect in economics and decided the best model between FDE, namely Adomian decomposition and Variational iterative methods using numerical analysis.Muhamad Deni JohansyahAsep K. SupriatnaEndang RusyamanJumadil SaputraGrowing SciencearticleAnalysisQA299.6-433Business mathematics. Commercial arithmetic. Including tables, etc.HF5691-5716ENDecision Science Letters, Vol 11, Iss 1, Pp 73-80 (2022)
institution DOAJ
collection DOAJ
language EN
topic Analysis
QA299.6-433
Business mathematics. Commercial arithmetic. Including tables, etc.
HF5691-5716
spellingShingle Analysis
QA299.6-433
Business mathematics. Commercial arithmetic. Including tables, etc.
HF5691-5716
Muhamad Deni Johansyah
Asep K. Supriatna
Endang Rusyaman
Jumadil Saputra
Modelling of natural growth with memory effect in economics: An application of adomian decomposition and variational iteration methods
description The power-law memory effect is taken into consideration in a generalisation of the economic model of natural growth. The memory effect refers to a process's reliance on its current state and its history of previous changes. However, the study that focuses on natural growth in economics considering the memory effect with fractional order-linear differential equation model is still limited. The current investigation seeks to solve the natural growth with memory effect in the economics model and decide the best model using fractional differential equation (FDE), namely Adomian Decomposition and Variational Iteration Methods. Also, this study assumes the level of consumer loss memory during a certain time interval denoted by a parameter (α). This study showed the model of loss memory effect with 0 < α ≤ 1 given a slowdown in output growth compared to a model without memory effect. Besides that, this study also found that output Y(t) is growing faster with the Variational Iteration method compared to the Adomian decomposition method. Also, using graphical simulation, this study found the output Y(t) is closer to the exact solution with α=0.4 and α=0.9. In conclusion, this study successfully solved natural growth with memory effect in economics and decided the best model between FDE, namely Adomian decomposition and Variational iterative methods using numerical analysis.
format article
author Muhamad Deni Johansyah
Asep K. Supriatna
Endang Rusyaman
Jumadil Saputra
author_facet Muhamad Deni Johansyah
Asep K. Supriatna
Endang Rusyaman
Jumadil Saputra
author_sort Muhamad Deni Johansyah
title Modelling of natural growth with memory effect in economics: An application of adomian decomposition and variational iteration methods
title_short Modelling of natural growth with memory effect in economics: An application of adomian decomposition and variational iteration methods
title_full Modelling of natural growth with memory effect in economics: An application of adomian decomposition and variational iteration methods
title_fullStr Modelling of natural growth with memory effect in economics: An application of adomian decomposition and variational iteration methods
title_full_unstemmed Modelling of natural growth with memory effect in economics: An application of adomian decomposition and variational iteration methods
title_sort modelling of natural growth with memory effect in economics: an application of adomian decomposition and variational iteration methods
publisher Growing Science
publishDate 2022
url https://doaj.org/article/10e954c29a5c4ac798d63c0c9be690c0
work_keys_str_mv AT muhamaddenijohansyah modellingofnaturalgrowthwithmemoryeffectineconomicsanapplicationofadomiandecompositionandvariationaliterationmethods
AT asepksupriatna modellingofnaturalgrowthwithmemoryeffectineconomicsanapplicationofadomiandecompositionandvariationaliterationmethods
AT endangrusyaman modellingofnaturalgrowthwithmemoryeffectineconomicsanapplicationofadomiandecompositionandvariationaliterationmethods
AT jumadilsaputra modellingofnaturalgrowthwithmemoryeffectineconomicsanapplicationofadomiandecompositionandvariationaliterationmethods
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