Convergence and Error Estimation of a New Formulation of Homotopy Perturbation Method for Classes of Nonlinear Integral/Integro-Differential Equations

Convergence and Error Estimation of a New Formulation of Homotopy Perturbation Method for Classes of Nonlinear Integral/Integro-Differential Equations

In this work, the main concept of the homotopy perturbation method (HPM) was outlined and convergence theorems of the HPM for solving some classes of nonlinear integral, integro-differential and differential equations were proved. A theorem for estimating the error in the approximate solution was pr...

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Main Authors: Mohamed M. Mousa, Fahad Alsharari
Format: Article
Language:English
Published: MDPI AG 2021-09-01
Series:Mathematics
Subjects:
homotopy perturbation method
nonlinear integral equation
nonlinear integro-differential equation
error estimation
Online Access:https://www.mdpi.com/2227-7390/9/18/2244
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spelling doaj-ddd0867f175a4e10ac5541bb9548bfaf2021-09-26T00:38:10ZengMDPI AGMathematics2227-73902021-09-0192244224410.3390/math9182244Convergence and Error Estimation of a New Formulation of Homotopy Perturbation Method for Classes of Nonlinear Integral/Integro-Differential EquationsMohamed M. Mousa0Fahad Alsharari1Department of Mathematics, College of Sciences and Human Studies at Hotat Sudair, Majmaah University, Al-Majmaah 11952, Saudi ArabiaDepartment of Mathematics, College of Sciences and Human Studies at Hotat Sudair, Majmaah University, Al-Majmaah 11952, Saudi ArabiaIn this work, the main concept of the homotopy perturbation method (HPM) was outlined and convergence theorems of the HPM for solving some classes of nonlinear integral, integro-differential and differential equations were proved. A theorem for estimating the error in the approximate solution was proved as well. The proposed HPM convergence theorems were confirmed and the efficiency of the technique was explored by applying the HPM for solving several classes of nonlinear integral/integro-differential equations.https://www.mdpi.com/2227-7390/9/18/2244homotopy perturbation methodnonlinear integral equationnonlinear integro-differential equationerror estimation
collection DOAJ
language English
format Article
sources DOAJ
author Mohamed M. Mousa
Fahad Alsharari
spellingShingle Mohamed M. Mousa
Fahad Alsharari
Convergence and Error Estimation of a New Formulation of Homotopy Perturbation Method for Classes of Nonlinear Integral/Integro-Differential Equations
Mathematics
homotopy perturbation method
nonlinear integral equation
nonlinear integro-differential equation
error estimation
author_facet Mohamed M. Mousa
Fahad Alsharari
author_sort Mohamed M. Mousa
title Convergence and Error Estimation of a New Formulation of Homotopy Perturbation Method for Classes of Nonlinear Integral/Integro-Differential Equations
title_short Convergence and Error Estimation of a New Formulation of Homotopy Perturbation Method for Classes of Nonlinear Integral/Integro-Differential Equations
title_full Convergence and Error Estimation of a New Formulation of Homotopy Perturbation Method for Classes of Nonlinear Integral/Integro-Differential Equations
title_fullStr Convergence and Error Estimation of a New Formulation of Homotopy Perturbation Method for Classes of Nonlinear Integral/Integro-Differential Equations
title_full_unstemmed Convergence and Error Estimation of a New Formulation of Homotopy Perturbation Method for Classes of Nonlinear Integral/Integro-Differential Equations
title_sort convergence and error estimation of a new formulation of homotopy perturbation method for classes of nonlinear integral/integro-differential equations
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2021-09-01
description In this work, the main concept of the homotopy perturbation method (HPM) was outlined and convergence theorems of the HPM for solving some classes of nonlinear integral, integro-differential and differential equations were proved. A theorem for estimating the error in the approximate solution was proved as well. The proposed HPM convergence theorems were confirmed and the efficiency of the technique was explored by applying the HPM for solving several classes of nonlinear integral/integro-differential equations.
topic homotopy perturbation method
nonlinear integral equation
nonlinear integro-differential equation
error estimation
url https://www.mdpi.com/2227-7390/9/18/2244
work_keys_str_mv AT mohamedmmousa convergenceanderrorestimationofanewformulationofhomotopyperturbationmethodforclassesofnonlinearintegralintegrodifferentialequations
AT fahadalsharari convergenceanderrorestimationofanewformulationofhomotopyperturbationmethodforclassesofnonlinearintegralintegrodifferentialequations
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