A New Approximation Method for Solving Fuzzy Heat Equations

A. F. Jameel; Nidal Anakira; A. K. Alomari; I. Hashim; Shaher Momani

doi:10.1166/jctn.2016.5784

A New Approximation Method for Solving Fuzzy Heat Equations

A. F. Jameel
, Nidal Anakira
, A. K. Alomari
, I. Hashim
, Shaher Momani

University Utara Malaysia
Irbid National University
Yarmouk University
Universiti Kebangsaan Malaysia
King Fahd University of Petroleum and Minerals
University of Jordan
Faculty of Sciences, King Abdulaziz University

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

In this paper, we develop and analyze the use of the Optimal Homotopy Asymptotic Method (OHAM) to find the approximate analytical solution for partial differential equation involving fuzzy heat equation. OHAM allows the solution of the partial differential equation to be calculated in the form of an infinite series in which the components can be easily computed. The convergence theorem of this method in fuzzy case is presented and proved. This method provides us with a convenient way to control the convergence of approximation series. The method is tested on linear fuzzy heat equations and comparing the exact solution that were made with numerical results showed the effectiveness and accuracy of this method.

Original language	English
Pages (from-to)	7825-7832
Number of pages	8
Journal	Journal of Computational and Theoretical Nanoscience
Volume	13
Issue number	11
DOIs	https://doi.org/10.1166/jctn.2016.5784
State	Published - 2016
Externally published	Yes

Keywords

Fuzzy differential equations
Fuzzy heat equation
Fuzzy numbers
Optimal homotopy asymptotic method

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10.1166/jctn.2016.5784

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title = "A New Approximation Method for Solving Fuzzy Heat Equations",

abstract = "In this paper, we develop and analyze the use of the Optimal Homotopy Asymptotic Method (OHAM) to find the approximate analytical solution for partial differential equation involving fuzzy heat equation. OHAM allows the solution of the partial differential equation to be calculated in the form of an infinite series in which the components can be easily computed. The convergence theorem of this method in fuzzy case is presented and proved. This method provides us with a convenient way to control the convergence of approximation series. The method is tested on linear fuzzy heat equations and comparing the exact solution that were made with numerical results showed the effectiveness and accuracy of this method.",

keywords = "Fuzzy differential equations, Fuzzy heat equation, Fuzzy numbers, Optimal homotopy asymptotic method",

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T1 - A New Approximation Method for Solving Fuzzy Heat Equations

AU - Jameel, A. F.

AU - Anakira, Nidal

AU - Alomari, A. K.

AU - Hashim, I.

AU - Momani, Shaher

PY - 2016

Y1 - 2016

N2 - In this paper, we develop and analyze the use of the Optimal Homotopy Asymptotic Method (OHAM) to find the approximate analytical solution for partial differential equation involving fuzzy heat equation. OHAM allows the solution of the partial differential equation to be calculated in the form of an infinite series in which the components can be easily computed. The convergence theorem of this method in fuzzy case is presented and proved. This method provides us with a convenient way to control the convergence of approximation series. The method is tested on linear fuzzy heat equations and comparing the exact solution that were made with numerical results showed the effectiveness and accuracy of this method.

AB - In this paper, we develop and analyze the use of the Optimal Homotopy Asymptotic Method (OHAM) to find the approximate analytical solution for partial differential equation involving fuzzy heat equation. OHAM allows the solution of the partial differential equation to be calculated in the form of an infinite series in which the components can be easily computed. The convergence theorem of this method in fuzzy case is presented and proved. This method provides us with a convenient way to control the convergence of approximation series. The method is tested on linear fuzzy heat equations and comparing the exact solution that were made with numerical results showed the effectiveness and accuracy of this method.

KW - Fuzzy differential equations

KW - Fuzzy heat equation

KW - Fuzzy numbers

KW - Optimal homotopy asymptotic method

UR - https://www.scopus.com/pages/publications/85015169702

U2 - 10.1166/jctn.2016.5784

DO - 10.1166/jctn.2016.5784

M3 - Article

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SN - 1546-1955

VL - 13

SP - 7825

EP - 7832

JO - Journal of Computational and Theoretical Nanoscience

JF - Journal of Computational and Theoretical Nanoscience

IS - 11

ER -

A New Approximation Method for Solving Fuzzy Heat Equations

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Keywords

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