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Approximate Solution of Linear Fuzzy Random Ordinary Differential Equations Using Laplace Variational Iteration Method.

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Τίτλος: Approximate Solution of Linear Fuzzy Random Ordinary Differential Equations Using Laplace Variational Iteration Method.
Alternate Title: الحل التقريبي للمعادلات التفاضلية الخطية الضبابية العشوائية الاعتيادية باستخدام طريقة لابلاس للتكرار المتغير. (Arabic)
Συγγραφείς: Abdulsahib, Ali Adnan, Fadhel, Fadhel S., Eidi, Jaafer Hmood
Πηγή: Iraqi Journal of Science; 2024, Vol. 65 Issue 2, p804-817, 14p
Θεματικοί όροι: Wiener processes, Lagrange multiplier, Stochastic processes, Ordinary differential equations, Laplace transformation, Computer software, Differential equations
Abstract (English): In this article, the Laplace transformation method in connection with the variational iteration method will be used to solve approximately fuzzy random ordinary differential equations. After that, the sequence of approximated closed form iterated solutions is derived based on the general Lagrange multiplier evaluated using the well-known convolution theorem of the Laplace transformation method. In addition, two examples are given and solved to illustrate the reliability, efficiency and applicability of the proposed method, they are simulated using computer programs with two different generations of stochastic processes, namely the Wiener process or Brownian motion, which are 1000 and 10000, respectively. [ABSTRACT FROM AUTHOR]
Abstract (Arabic): في هذه البحث، سنقدم طريقة تحويل لابلاس مع طريقة التكرار المتغير لايجاد الحل التقريبي للمعادلات التفاضلية الخطية الاعتيادية العشوائية الضبابية. حيث تم اشتقاق متتابعة دوال الحلول التقريبية استناداً الى ايجاد مضروب لاكرانج والذي تم حسابه عن طريق مبرهنة الالتفاف المعروفة في تحويلات لابلاس. إضافة إلى ذلك، تم تقديم مثالين وحلهما لتوضيح موثوقية وإمكانية تطبيق الطريقة المقترحة. بالإضافة إلى ذلك، تم تقديم مثالين وحلهما لبيان مدى موثوقية وكفاءة وإمكانية تطبيق الطريقة المقترحة، والتي تمت محاكاتها باستخدام برامج حاسوبية مع توليد مجموعتين مختلفين من المتغيرات التصادفية والتي تسمى متغيرات وينر التصادفية أو حركة براونين، وهما 1000 و 10000، على التوالي. [ABSTRACT FROM AUTHOR]
Copyright of Iraqi Journal of Science is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Approximate Solution of Linear Fuzzy Random Ordinary Differential Equations Using Laplace Variational Iteration Method.
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  Data: الحل التقريبي للمعادلات التفاضلية الخطية الضبابية العشوائية الاعتيادية باستخدام طريقة لابلاس للتكرار المتغير. (Arabic)
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  Data: <searchLink fieldCode="AR" term="%22Abdulsahib%2C+Ali+Adnan%22">Abdulsahib, Ali Adnan</searchLink><br /><searchLink fieldCode="AR" term="%22Fadhel%2C+Fadhel+S%2E%22">Fadhel, Fadhel S.</searchLink><br /><searchLink fieldCode="AR" term="%22Eidi%2C+Jaafer+Hmood%22">Eidi, Jaafer Hmood</searchLink>
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  Data: Iraqi Journal of Science; 2024, Vol. 65 Issue 2, p804-817, 14p
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  Data: <searchLink fieldCode="DE" term="%22Wiener+processes%22">Wiener processes</searchLink><br /><searchLink fieldCode="DE" term="%22Lagrange+multiplier%22">Lagrange multiplier</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+processes%22">Stochastic processes</searchLink><br /><searchLink fieldCode="DE" term="%22Ordinary+differential+equations%22">Ordinary differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Laplace+transformation%22">Laplace transformation</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+software%22">Computer software</searchLink><br /><searchLink fieldCode="DE" term="%22Differential+equations%22">Differential equations</searchLink>
– Name: AbstractNonEng
  Label: Abstract (English)
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  Data: In this article, the Laplace transformation method in connection with the variational iteration method will be used to solve approximately fuzzy random ordinary differential equations. After that, the sequence of approximated closed form iterated solutions is derived based on the general Lagrange multiplier evaluated using the well-known convolution theorem of the Laplace transformation method. In addition, two examples are given and solved to illustrate the reliability, efficiency and applicability of the proposed method, they are simulated using computer programs with two different generations of stochastic processes, namely the Wiener process or Brownian motion, which are 1000 and 10000, respectively. [ABSTRACT FROM AUTHOR]
– Name: AbstractNonEng
  Label: Abstract (Arabic)
  Group: Ab
  Data: في هذه البحث، سنقدم طريقة تحويل لابلاس مع طريقة التكرار المتغير لايجاد الحل التقريبي للمعادلات التفاضلية الخطية الاعتيادية العشوائية الضبابية. حيث تم اشتقاق متتابعة دوال الحلول التقريبية استناداً الى ايجاد مضروب لاكرانج والذي تم حسابه عن طريق مبرهنة الالتفاف المعروفة في تحويلات لابلاس. إضافة إلى ذلك، تم تقديم مثالين وحلهما لتوضيح موثوقية وإمكانية تطبيق الطريقة المقترحة. بالإضافة إلى ذلك، تم تقديم مثالين وحلهما لبيان مدى موثوقية وكفاءة وإمكانية تطبيق الطريقة المقترحة، والتي تمت محاكاتها باستخدام برامج حاسوبية مع توليد مجموعتين مختلفين من المتغيرات التصادفية والتي تسمى متغيرات وينر التصادفية أو حركة براونين، وهما 1000 و 10000، على التوالي. [ABSTRACT FROM AUTHOR]
– Name: Abstract
  Label:
  Group: Ab
  Data: <i>Copyright of Iraqi Journal of Science is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.24996/ijs.2024.65.2.18
    Languages:
      – Code: eng
        Text: English
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      Pagination:
        PageCount: 14
        StartPage: 804
    Subjects:
      – SubjectFull: Wiener processes
        Type: general
      – SubjectFull: Lagrange multiplier
        Type: general
      – SubjectFull: Stochastic processes
        Type: general
      – SubjectFull: Ordinary differential equations
        Type: general
      – SubjectFull: Laplace transformation
        Type: general
      – SubjectFull: Computer software
        Type: general
      – SubjectFull: Differential equations
        Type: general
    Titles:
      – TitleFull: Approximate Solution of Linear Fuzzy Random Ordinary Differential Equations Using Laplace Variational Iteration Method.
        Type: main
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            NameFull: Abdulsahib, Ali Adnan
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            NameFull: Fadhel, Fadhel S.
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            NameFull: Eidi, Jaafer Hmood
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              M: 02
              Text: 2024
              Type: published
              Y: 2024
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              Value: 65
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            – TitleFull: Iraqi Journal of Science
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