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Integral iterative method for solving Newell-Whitehead-Segel equation / Nur' Atikah Khusairi, Nurul Izzaty Abdul Ghafar and Siti Nur Syafiqah Syed Huzaini

In this paper, the Integral Iterative Method (IIM) was execute for form exact solutions of the Newell-Whitehead-Segel equation. Newell-Whitehead-Segel equation can be recognized as nonlinear equation of an important model arising in fluid mechanics. But a nonlinear problem that contained strong nonl...

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Main Authors: Khusairi, Nur' Atikah, Abdul Ghafar, Nurul Izzaty, Syed Huzaini, Siti Nur Syafiqah
Format: Student Project
Language:English
Published: 2019
Subjects:
Study and teaching
Mathematical statistics. Probabilities
Analytical methods used in the solution of physical problems
Online Access:http://ir.uitm.edu.my/id/eprint/39138/1/39138.pdf
http://ir.uitm.edu.my/id/eprint/39138/
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spelling my.uitm.ir.391382020-12-24T03:54:00Z http://ir.uitm.edu.my/id/eprint/39138/ Integral iterative method for solving Newell-Whitehead-Segel equation / Nur' Atikah Khusairi, Nurul Izzaty Abdul Ghafar and Siti Nur Syafiqah Syed Huzaini Khusairi, Nur' Atikah Abdul Ghafar, Nurul Izzaty Syed Huzaini, Siti Nur Syafiqah Study and teaching Mathematical statistics. Probabilities Analytical methods used in the solution of physical problems In this paper, the Integral Iterative Method (IIM) was execute for form exact solutions of the Newell-Whitehead-Segel equation. Newell-Whitehead-Segel equation can be recognized as nonlinear equation of an important model arising in fluid mechanics. But a nonlinear problem that contained strong nonlinearity and many are unknown. Usually, the iteration method would be used to solve nonlinear problems, but the convergence of iterations methods is very difficult to be achieved. The main objective of this report is approximating accuracy, reliability and ef¬ ficiency of JIM, when comparing Adomian Decomposition Method (ADM), Laplace Adomian Decomposition Method (LADM) and New Iterative Method (NIM). There are three problems of Newell-Whitehead-Segel equation chosen to be presented in an effective way. Numerous methods such as Variational Iteration Method (YIM), Homotopy Perturbation Method (HPM), and more methods have been used to solve this equation. However, in this paper, this equation is resolved using IIM. Our results show that IIM will be accurate, convenient and reliable in solving the nonlinear problems. IIM and were compared with the LADM, ADM and NIM, show the ability of Newell-Whitehead-Segel equation in solving nonlinear partial differential.Overall, this report made several contributions of Newell-Whitehead-Segel equation using IIM.First, for the first time, it is shown that IIM is better compared to NIM and LADM, which is absolutely convergence for the range of utility of the power series and closest to zero for the result of error value. Second, it is demonstrated that the error of JIM and NIM are compatible since the value of u(x,t) are close to zero compared to ADM. Third, it is concluded that HM solution could generate the same results with the exact solution. Based on the calculation, JIM is simpler and efficient implement for resolve varied category of non-linear differential and in¬ tegral equations, since this method only use direct integration method to derive the solution and the results were successfully explained. 2019 Student Project NonPeerReviewed text en http://ir.uitm.edu.my/id/eprint/39138/1/39138.pdf Khusairi, Nur' Atikah and Abdul Ghafar, Nurul Izzaty and Syed Huzaini, Siti Nur Syafiqah (2019) Integral iterative method for solving Newell-Whitehead-Segel equation / Nur' Atikah Khusairi, Nurul Izzaty Abdul Ghafar and Siti Nur Syafiqah Syed Huzaini. [Student Project] (Unpublished)
institution Universiti Teknologi Mara
building Tun Abdul Razak Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Teknologi Mara
content_source UiTM Institutional Repository
url_provider http://ir.uitm.edu.my/
language English
topic Study and teaching
Mathematical statistics. Probabilities
Analytical methods used in the solution of physical problems
spellingShingle Study and teaching
Mathematical statistics. Probabilities
Analytical methods used in the solution of physical problems
Khusairi, Nur' Atikah
Abdul Ghafar, Nurul Izzaty
Syed Huzaini, Siti Nur Syafiqah
Integral iterative method for solving Newell-Whitehead-Segel equation / Nur' Atikah Khusairi, Nurul Izzaty Abdul Ghafar and Siti Nur Syafiqah Syed Huzaini
description In this paper, the Integral Iterative Method (IIM) was execute for form exact solutions of the Newell-Whitehead-Segel equation. Newell-Whitehead-Segel equation can be recognized as nonlinear equation of an important model arising in fluid mechanics. But a nonlinear problem that contained strong nonlinearity and many are unknown. Usually, the iteration method would be used to solve nonlinear problems, but the convergence of iterations methods is very difficult to be achieved. The main objective of this report is approximating accuracy, reliability and ef¬ ficiency of JIM, when comparing Adomian Decomposition Method (ADM), Laplace Adomian Decomposition Method (LADM) and New Iterative Method (NIM). There are three problems of Newell-Whitehead-Segel equation chosen to be presented in an effective way. Numerous methods such as Variational Iteration Method (YIM), Homotopy Perturbation Method (HPM), and more methods have been used to solve this equation. However, in this paper, this equation is resolved using IIM. Our results show that IIM will be accurate, convenient and reliable in solving the nonlinear problems. IIM and were compared with the LADM, ADM and NIM, show the ability of Newell-Whitehead-Segel equation in solving nonlinear partial differential.Overall, this report made several contributions of Newell-Whitehead-Segel equation using IIM.First, for the first time, it is shown that IIM is better compared to NIM and LADM, which is absolutely convergence for the range of utility of the power series and closest to zero for the result of error value. Second, it is demonstrated that the error of JIM and NIM are compatible since the value of u(x,t) are close to zero compared to ADM. Third, it is concluded that HM solution could generate the same results with the exact solution. Based on the calculation, JIM is simpler and efficient implement for resolve varied category of non-linear differential and in¬ tegral equations, since this method only use direct integration method to derive the solution and the results were successfully explained.
format Student Project
author Khusairi, Nur' Atikah
Abdul Ghafar, Nurul Izzaty
Syed Huzaini, Siti Nur Syafiqah
author_facet Khusairi, Nur' Atikah
Abdul Ghafar, Nurul Izzaty
Syed Huzaini, Siti Nur Syafiqah
author_sort Khusairi, Nur' Atikah
title Integral iterative method for solving Newell-Whitehead-Segel equation / Nur' Atikah Khusairi, Nurul Izzaty Abdul Ghafar and Siti Nur Syafiqah Syed Huzaini
title_short Integral iterative method for solving Newell-Whitehead-Segel equation / Nur' Atikah Khusairi, Nurul Izzaty Abdul Ghafar and Siti Nur Syafiqah Syed Huzaini
title_full Integral iterative method for solving Newell-Whitehead-Segel equation / Nur' Atikah Khusairi, Nurul Izzaty Abdul Ghafar and Siti Nur Syafiqah Syed Huzaini
title_fullStr Integral iterative method for solving Newell-Whitehead-Segel equation / Nur' Atikah Khusairi, Nurul Izzaty Abdul Ghafar and Siti Nur Syafiqah Syed Huzaini
title_full_unstemmed Integral iterative method for solving Newell-Whitehead-Segel equation / Nur' Atikah Khusairi, Nurul Izzaty Abdul Ghafar and Siti Nur Syafiqah Syed Huzaini
title_sort integral iterative method for solving newell-whitehead-segel equation / nur' atikah khusairi, nurul izzaty abdul ghafar and siti nur syafiqah syed huzaini
publishDate 2019
url http://ir.uitm.edu.my/id/eprint/39138/1/39138.pdf
http://ir.uitm.edu.my/id/eprint/39138/
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score 13.211869

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