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
Materias:	Analysis QA299.6-433 Business mathematics. Commercial arithmetic. Including tables, etc. HF5691-5716
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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Modelling of natural growth with memory effect in economics: An application of adomian decomposition and variational iteration methods

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