A linearization-based computational algorithm of homotopy analysis method for nonlinear reaction–diffusion systems

In this study, an optimal homotopy analysis algorithm is outlined by means of the nonlinear reaction–diffusion systems. This algorithm, the linearization-based algorithm, employs Taylor series approximations of the nonlinear equations to construct an optimal decomposition of the homotopy series solu...

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Vydané v:Mathematics and computers in simulation Ročník 194; s. 505 - 522
Hlavní autori: Al-Qudah, Alaa, Odibat, Zaid, Shawagfeh, Nabil
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier B.V 01.04.2022
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ISSN:0378-4754, 1872-7166
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Abstract In this study, an optimal homotopy analysis algorithm is outlined by means of the nonlinear reaction–diffusion systems. This algorithm, the linearization-based algorithm, employs Taylor series approximations of the nonlinear equations to construct an optimal decomposition of the homotopy series solutions. Numerical comparisons between the proposed algorithm and the standard homotopy approach, as tools for analytically solving reaction–diffusion systems, are performed to test the computational efficiency and the pertinent features of the suggested algorithm. The illustrated numerical results demonstrate that the linearization-based algorithm improves the accuracy and the convergence of the homotopy series solutions. The suggested algorithm can be further used to get rapid convergent series solutions for different types of systems of partial differential equations.
AbstractList In this study, an optimal homotopy analysis algorithm is outlined by means of the nonlinear reaction–diffusion systems. This algorithm, the linearization-based algorithm, employs Taylor series approximations of the nonlinear equations to construct an optimal decomposition of the homotopy series solutions. Numerical comparisons between the proposed algorithm and the standard homotopy approach, as tools for analytically solving reaction–diffusion systems, are performed to test the computational efficiency and the pertinent features of the suggested algorithm. The illustrated numerical results demonstrate that the linearization-based algorithm improves the accuracy and the convergence of the homotopy series solutions. The suggested algorithm can be further used to get rapid convergent series solutions for different types of systems of partial differential equations.
Author Shawagfeh, Nabil
Odibat, Zaid
Al-Qudah, Alaa
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Cites_doi 10.1016/j.cnsns.2009.09.002
10.1016/j.apm.2015.02.025
10.1016/j.cnsns.2008.07.010
10.1016/j.cnsns.2017.05.005
10.1016/j.nonrwa.2008.04.018
10.1016/0375-9601(96)00102-8
10.1016/j.asej.2013.07.004
10.1016/j.apm.2015.10.005
10.1016/j.cnsns.2009.03.008
10.1016/j.nonrwa.2007.10.014
10.1016/j.cnsns.2008.04.013
10.1002/mma.3136
10.1016/j.nonrwa.2013.06.003
10.1111/j.1467-9590.2007.00387.x
10.1016/j.apm.2012.08.023
10.1002/mma.5829
10.1016/S1007-5704(97)90047-2
10.1016/j.cej.2007.03.022
10.1016/j.jmaa.2020.124089
10.1016/j.physleta.2007.04.070
10.1016/j.ymssp.2014.07.013
10.1088/1402-4896/ab7b8a
10.1016/j.apnum.2018.11.003
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Keywords Reaction–diffusion system
Linearization-based algorithm
Homotopy analysis method
Series solution
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References Rashidi, Dinarvand (b28) 2009; 10
Liao (b15) 2010; 15
Odibat, Bataineh (b25) 2015; 38
Liao (b12) 2003
Odibat (b21) 2010; 217
Odibat, Baleanu (b24) 2019; 42
Sardanyes, Rodrigues, Janurio, Martins, Gil-Gmez, Duarte (b29) 2015; 252
Odibat, Kumar (b26) 2019; 14
Wang, Zou, Zhang (b31) 2007; 369
Martin (b18) 2013; 37
Liao (b14) 2009; 14
Kriete, Eils (b9) 2006
Gorder, Vajravelu (b6) 2009; 14
Feng (b5) 1996; 213
Hetmaniok, Słota, Wituła, Zielonka (b8) 2015; 39
Liu, Liu, Chen (b17) 2016; 40
Grindrod (b7) 1996
Odibat (b22) 2019; 137
Odibat, Shawagfeh (b27) 2020; 95
Cantrell, Cosner (b3) 2003
Britton (b2) 1986
Molabahrami, Khani (b20) 2009; 10
Abbasbandy (b1) 2008; 136
Chen, Liu (b4) 2009; 14
Kumar, Singh, Kumar, Kapoor (b10) 2014; 5
Shivanian, Abbasbandy (b30) 2014; 15
Massa, Lallemand, Tison (b19) 2015; 52
Liao (b11) 1997; 2
Yang, Liao (b32) 2017; 53
Odibat (b23) 2020; 488
Liao (b13) 2004; 147
Liao, Tan (b16) 2007; 119
Cantrell (10.1016/j.matcom.2021.11.027_b3) 2003
Liao (10.1016/j.matcom.2021.11.027_b12) 2003
Martin (10.1016/j.matcom.2021.11.027_b18) 2013; 37
Liu (10.1016/j.matcom.2021.11.027_b17) 2016; 40
Odibat (10.1016/j.matcom.2021.11.027_b27) 2020; 95
Kumar (10.1016/j.matcom.2021.11.027_b10) 2014; 5
Odibat (10.1016/j.matcom.2021.11.027_b22) 2019; 137
Rashidi (10.1016/j.matcom.2021.11.027_b28) 2009; 10
Yang (10.1016/j.matcom.2021.11.027_b32) 2017; 53
Grindrod (10.1016/j.matcom.2021.11.027_b7) 1996
Sardanyes (10.1016/j.matcom.2021.11.027_b29) 2015; 252
Shivanian (10.1016/j.matcom.2021.11.027_b30) 2014; 15
Odibat (10.1016/j.matcom.2021.11.027_b23) 2020; 488
Chen (10.1016/j.matcom.2021.11.027_b4) 2009; 14
Hetmaniok (10.1016/j.matcom.2021.11.027_b8) 2015; 39
Kriete (10.1016/j.matcom.2021.11.027_b9) 2006
Odibat (10.1016/j.matcom.2021.11.027_b25) 2015; 38
Gorder (10.1016/j.matcom.2021.11.027_b6) 2009; 14
Liao (10.1016/j.matcom.2021.11.027_b14) 2009; 14
Molabahrami (10.1016/j.matcom.2021.11.027_b20) 2009; 10
Feng (10.1016/j.matcom.2021.11.027_b5) 1996; 213
Odibat (10.1016/j.matcom.2021.11.027_b21) 2010; 217
Britton (10.1016/j.matcom.2021.11.027_b2) 1986
Liao (10.1016/j.matcom.2021.11.027_b11) 1997; 2
Liao (10.1016/j.matcom.2021.11.027_b15) 2010; 15
Liao (10.1016/j.matcom.2021.11.027_b16) 2007; 119
Odibat (10.1016/j.matcom.2021.11.027_b24) 2019; 42
Wang (10.1016/j.matcom.2021.11.027_b31) 2007; 369
Massa (10.1016/j.matcom.2021.11.027_b19) 2015; 52
Liao (10.1016/j.matcom.2021.11.027_b13) 2004; 147
Abbasbandy (10.1016/j.matcom.2021.11.027_b1) 2008; 136
Odibat (10.1016/j.matcom.2021.11.027_b26) 2019; 14
References_xml – volume: 119
  start-page: 297
  year: 2007
  end-page: 354
  ident: b16
  article-title: A general approach to obtain series solutions of nonlinear differential equations
  publication-title: Stud. Appl. Math.
– volume: 10
  start-page: 2346
  year: 2009
  end-page: 2356
  ident: b28
  article-title: Purely analytic approximate solutions for steady three-dimensional problem of condensation film on inclined rotating disk by homotopy analysis method
  publication-title: Nonlinear Anal. RWA
– volume: 137
  start-page: 203
  year: 2019
  end-page: 212
  ident: b22
  article-title: On the optimal selection of the linear operator and the initial approximation in the application of the homotopy analysis method to nonlinear fractional differential equations
  publication-title: Appl. Numer. Math.
– volume: 42
  start-page: 7222
  year: 2019
  end-page: 7232
  ident: b24
  article-title: A linearization-based approach of homotopy analysis method for non-linear time-fractional parabolic PDEs
  publication-title: Math. Methods Appl. Sci.
– volume: 488
  year: 2020
  ident: b23
  article-title: An improved optimal homotopy analysis algorithm for nonlinear differential equations
  publication-title: J. Math. Anal. Appl.
– volume: 14
  year: 2019
  ident: b26
  article-title: A robust computational algorithm of homotopy asymptotic method for solving systems of fractional differential equations
  publication-title: J. Comput. Nonlinear Dyn.
– volume: 95
  year: 2020
  ident: b27
  article-title: An optimal linearization-based predictor–corrector algorithm for the simulation of nonlinear FDEs
  publication-title: Phys. Scr.
– volume: 53
  start-page: 249
  year: 2017
  end-page: 262
  ident: b32
  article-title: A HAM-based wavelet approach for nonlinear partial differential equations: Two dimensional Bratu problem as an application
  publication-title: Comm. Nonlinear Sci. Numer. Simul.
– volume: 15
  start-page: 2003
  year: 2010
  end-page: 2016
  ident: b15
  article-title: An optimal homotopy-analysis approach for strongly nonlinear differential equations
  publication-title: Comm. Nonlinear Sci. Numer. Simul.
– year: 2003
  ident: b12
  article-title: Beyond Perturbation: Introduction to the Homotopy Analysis Method
– volume: 37
  start-page: 3959
  year: 2013
  end-page: 3967
  ident: b18
  article-title: On the homotopy analysis method for solving a particle transport equation
  publication-title: Appl. Math. Model.
– volume: 217
  start-page: 782
  year: 2010
  end-page: 789
  ident: b21
  article-title: Astudy on the convergence of homotopy analysis method
  publication-title: Appl. Math. Comput.
– volume: 5
  start-page: 243
  year: 2014
  end-page: 246
  ident: b10
  article-title: New homotopy analysis transform algorithm to solve Volterra integral equation
  publication-title: Ain Shams Eng. J.
– volume: 14
  start-page: 1816
  year: 2009
  end-page: 1821
  ident: b4
  article-title: A study of homotopy analysis method for limit cycle of van der pol equation
  publication-title: Comm. Nonlinear Sci. Numer. Simul.
– volume: 14
  start-page: 983
  year: 2009
  end-page: 997
  ident: b14
  article-title: Notes on the homotopy analysis method: Some definitions and theorems
  publication-title: Commun. Nonlinear Sci. Numer. Simul.
– year: 2003
  ident: b3
  article-title: Spatial Ecology Via Reaction–Diffusion Equations
– volume: 252
  start-page: 484
  year: 2015
  end-page: 495
  ident: b29
  article-title: Activation of effector immune cells promotes tumor stochastic extinction: A homotopy analysis approach
  publication-title: Appl. Math. Comput.
– volume: 136
  start-page: 144
  year: 2008
  end-page: 150
  ident: b1
  article-title: Approximate solution for the nonlinear model of diffusion and reaction in porous catalysts by means of the homotopy analysis method
  publication-title: Chem. Eng. J.
– volume: 213
  start-page: 167
  year: 1996
  end-page: 176
  ident: b5
  article-title: Exact wave front solutions to two generalized coupled nonlinear physical equations
  publication-title: Phys. Lett. A
– volume: 14
  start-page: 4078
  year: 2009
  end-page: 4089
  ident: b6
  article-title: On the selection of auxiliary functions, operators, and convergence control parameters in the application of the homotopy analysis method to nonlinear differential equations: a general approach
  publication-title: Comm. Nonlinear Sci. Numer. Simul.
– volume: 38
  start-page: 991
  year: 2015
  end-page: 1000
  ident: b25
  article-title: An adaptation of HAM for reliable treatment of strongly nonlinear problems: Construction of homotopy polynomials
  publication-title: Math. Methods Appl. Sci.
– year: 1986
  ident: b2
  article-title: Reaction–Diffusion Equations and Their Applications to Biology
– volume: 52
  start-page: 88
  year: 2015
  end-page: 104
  ident: b19
  article-title: Multi-level homotopy perturbation and projection techniques for the reanalysis of quadratic eigenvalue problems: The application of stability analysis
  publication-title: Mech. Syst. Signal Process.
– volume: 10
  start-page: 589
  year: 2009
  end-page: 600
  ident: b20
  article-title: The homotopy analysis method to solve the Burgers-Huxley equation
  publication-title: Nonlinear Anal. RWA
– volume: 15
  start-page: 89
  year: 2014
  end-page: 99
  ident: b30
  article-title: Predictor homotopy analysis method: Two points second order boundary value problems
  publication-title: Nonlinear Anal. RWA
– volume: 40
  start-page: 3211
  year: 2016
  end-page: 3220
  ident: b17
  article-title: Asymptotic limit cycle of fractional van der pol oscillator by homotopy analysis method and memory-free principle
  publication-title: Appl. Math. Model.
– volume: 369
  start-page: 77
  year: 2007
  end-page: 84
  ident: b31
  article-title: Applying homotopy analysis method for solving differential-difference equation
  publication-title: Phys. Lett. A
– volume: 2
  start-page: 95
  year: 1997
  end-page: 100
  ident: b11
  article-title: Homotopy analysis method: A new analytical technique for nonlinear problems
  publication-title: Commun. Nonlinear Sci. Numer. Simul.
– year: 1996
  ident: b7
  article-title: The Theory and Applications of Reaction–Diffusion Equations: Patterns and Waves
– volume: 147
  start-page: 499
  year: 2004
  end-page: 513
  ident: b13
  article-title: On the homotopy analysis method for nonlinear problems
  publication-title: Appl. Math. Comput.
– year: 2006
  ident: b9
  article-title: Computational Systems Biology
– volume: 39
  start-page: 6793
  year: 2015
  end-page: 6805
  ident: b8
  article-title: Solution of the one-phase inverse stefan problem by using the homotopy analysis method
  publication-title: Appl. Math. Model.
– volume: 15
  start-page: 2003
  issue: 8
  year: 2010
  ident: 10.1016/j.matcom.2021.11.027_b15
  article-title: An optimal homotopy-analysis approach for strongly nonlinear differential equations
  publication-title: Comm. Nonlinear Sci. Numer. Simul.
  doi: 10.1016/j.cnsns.2009.09.002
– volume: 39
  start-page: 6793
  issue: 22
  year: 2015
  ident: 10.1016/j.matcom.2021.11.027_b8
  article-title: Solution of the one-phase inverse stefan problem by using the homotopy analysis method
  publication-title: Appl. Math. Model.
  doi: 10.1016/j.apm.2015.02.025
– volume: 14
  start-page: 1816
  issue: 5
  year: 2009
  ident: 10.1016/j.matcom.2021.11.027_b4
  article-title: A study of homotopy analysis method for limit cycle of van der pol equation
  publication-title: Comm. Nonlinear Sci. Numer. Simul.
  doi: 10.1016/j.cnsns.2008.07.010
– year: 1986
  ident: 10.1016/j.matcom.2021.11.027_b2
– volume: 53
  start-page: 249
  year: 2017
  ident: 10.1016/j.matcom.2021.11.027_b32
  article-title: A HAM-based wavelet approach for nonlinear partial differential equations: Two dimensional Bratu problem as an application
  publication-title: Comm. Nonlinear Sci. Numer. Simul.
  doi: 10.1016/j.cnsns.2017.05.005
– year: 2003
  ident: 10.1016/j.matcom.2021.11.027_b3
– volume: 252
  start-page: 484
  issue: 1
  year: 2015
  ident: 10.1016/j.matcom.2021.11.027_b29
  article-title: Activation of effector immune cells promotes tumor stochastic extinction: A homotopy analysis approach
  publication-title: Appl. Math. Comput.
– volume: 217
  start-page: 782
  issue: 2
  year: 2010
  ident: 10.1016/j.matcom.2021.11.027_b21
  article-title: Astudy on the convergence of homotopy analysis method
  publication-title: Appl. Math. Comput.
– volume: 10
  start-page: 2346
  issue: 4
  year: 2009
  ident: 10.1016/j.matcom.2021.11.027_b28
  article-title: Purely analytic approximate solutions for steady three-dimensional problem of condensation film on inclined rotating disk by homotopy analysis method
  publication-title: Nonlinear Anal. RWA
  doi: 10.1016/j.nonrwa.2008.04.018
– volume: 213
  start-page: 167
  issue: 3–4
  year: 1996
  ident: 10.1016/j.matcom.2021.11.027_b5
  article-title: Exact wave front solutions to two generalized coupled nonlinear physical equations
  publication-title: Phys. Lett. A
  doi: 10.1016/0375-9601(96)00102-8
– volume: 5
  start-page: 243
  issue: 1
  year: 2014
  ident: 10.1016/j.matcom.2021.11.027_b10
  article-title: New homotopy analysis transform algorithm to solve Volterra integral equation
  publication-title: Ain Shams Eng. J.
  doi: 10.1016/j.asej.2013.07.004
– volume: 40
  start-page: 3211
  issue: 4
  year: 2016
  ident: 10.1016/j.matcom.2021.11.027_b17
  article-title: Asymptotic limit cycle of fractional van der pol oscillator by homotopy analysis method and memory-free principle
  publication-title: Appl. Math. Model.
  doi: 10.1016/j.apm.2015.10.005
– volume: 14
  start-page: 4078
  issue: 12
  year: 2009
  ident: 10.1016/j.matcom.2021.11.027_b6
  article-title: On the selection of auxiliary functions, operators, and convergence control parameters in the application of the homotopy analysis method to nonlinear differential equations: a general approach
  publication-title: Comm. Nonlinear Sci. Numer. Simul.
  doi: 10.1016/j.cnsns.2009.03.008
– year: 2003
  ident: 10.1016/j.matcom.2021.11.027_b12
– volume: 147
  start-page: 499
  issue: 2
  year: 2004
  ident: 10.1016/j.matcom.2021.11.027_b13
  article-title: On the homotopy analysis method for nonlinear problems
  publication-title: Appl. Math. Comput.
– volume: 10
  start-page: 589
  issue: 2
  year: 2009
  ident: 10.1016/j.matcom.2021.11.027_b20
  article-title: The homotopy analysis method to solve the Burgers-Huxley equation
  publication-title: Nonlinear Anal. RWA
  doi: 10.1016/j.nonrwa.2007.10.014
– volume: 14
  start-page: 983
  issue: 4
  year: 2009
  ident: 10.1016/j.matcom.2021.11.027_b14
  article-title: Notes on the homotopy analysis method: Some definitions and theorems
  publication-title: Commun. Nonlinear Sci. Numer. Simul.
  doi: 10.1016/j.cnsns.2008.04.013
– year: 2006
  ident: 10.1016/j.matcom.2021.11.027_b9
– volume: 38
  start-page: 991
  issue: 5
  year: 2015
  ident: 10.1016/j.matcom.2021.11.027_b25
  article-title: An adaptation of HAM for reliable treatment of strongly nonlinear problems: Construction of homotopy polynomials
  publication-title: Math. Methods Appl. Sci.
  doi: 10.1002/mma.3136
– volume: 15
  start-page: 89
  year: 2014
  ident: 10.1016/j.matcom.2021.11.027_b30
  article-title: Predictor homotopy analysis method: Two points second order boundary value problems
  publication-title: Nonlinear Anal. RWA
  doi: 10.1016/j.nonrwa.2013.06.003
– volume: 119
  start-page: 297
  issue: 4
  year: 2007
  ident: 10.1016/j.matcom.2021.11.027_b16
  article-title: A general approach to obtain series solutions of nonlinear differential equations
  publication-title: Stud. Appl. Math.
  doi: 10.1111/j.1467-9590.2007.00387.x
– volume: 37
  start-page: 3959
  issue: 6
  year: 2013
  ident: 10.1016/j.matcom.2021.11.027_b18
  article-title: On the homotopy analysis method for solving a particle transport equation
  publication-title: Appl. Math. Model.
  doi: 10.1016/j.apm.2012.08.023
– volume: 42
  start-page: 7222
  year: 2019
  ident: 10.1016/j.matcom.2021.11.027_b24
  article-title: A linearization-based approach of homotopy analysis method for non-linear time-fractional parabolic PDEs
  publication-title: Math. Methods Appl. Sci.
  doi: 10.1002/mma.5829
– volume: 14
  issue: 8
  year: 2019
  ident: 10.1016/j.matcom.2021.11.027_b26
  article-title: A robust computational algorithm of homotopy asymptotic method for solving systems of fractional differential equations
  publication-title: J. Comput. Nonlinear Dyn.
– volume: 2
  start-page: 95
  issue: 2
  year: 1997
  ident: 10.1016/j.matcom.2021.11.027_b11
  article-title: Homotopy analysis method: A new analytical technique for nonlinear problems
  publication-title: Commun. Nonlinear Sci. Numer. Simul.
  doi: 10.1016/S1007-5704(97)90047-2
– volume: 136
  start-page: 144
  issue: 2–3
  year: 2008
  ident: 10.1016/j.matcom.2021.11.027_b1
  article-title: Approximate solution for the nonlinear model of diffusion and reaction in porous catalysts by means of the homotopy analysis method
  publication-title: Chem. Eng. J.
  doi: 10.1016/j.cej.2007.03.022
– year: 1996
  ident: 10.1016/j.matcom.2021.11.027_b7
– volume: 488
  year: 2020
  ident: 10.1016/j.matcom.2021.11.027_b23
  article-title: An improved optimal homotopy analysis algorithm for nonlinear differential equations
  publication-title: J. Math. Anal. Appl.
  doi: 10.1016/j.jmaa.2020.124089
– volume: 369
  start-page: 77
  issue: 1–2
  year: 2007
  ident: 10.1016/j.matcom.2021.11.027_b31
  article-title: Applying homotopy analysis method for solving differential-difference equation
  publication-title: Phys. Lett. A
  doi: 10.1016/j.physleta.2007.04.070
– volume: 52
  start-page: 88
  year: 2015
  ident: 10.1016/j.matcom.2021.11.027_b19
  article-title: Multi-level homotopy perturbation and projection techniques for the reanalysis of quadratic eigenvalue problems: The application of stability analysis
  publication-title: Mech. Syst. Signal Process.
  doi: 10.1016/j.ymssp.2014.07.013
– volume: 95
  issue: 6
  year: 2020
  ident: 10.1016/j.matcom.2021.11.027_b27
  article-title: An optimal linearization-based predictor–corrector algorithm for the simulation of nonlinear FDEs
  publication-title: Phys. Scr.
  doi: 10.1088/1402-4896/ab7b8a
– volume: 137
  start-page: 203
  year: 2019
  ident: 10.1016/j.matcom.2021.11.027_b22
  article-title: On the optimal selection of the linear operator and the initial approximation in the application of the homotopy analysis method to nonlinear fractional differential equations
  publication-title: Appl. Numer. Math.
  doi: 10.1016/j.apnum.2018.11.003
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Snippet In this study, an optimal homotopy analysis algorithm is outlined by means of the nonlinear reaction–diffusion systems. This algorithm, the linearization-based...
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StartPage 505
SubjectTerms Homotopy analysis method
Linearization-based algorithm
Reaction–diffusion system
Series solution
Title A linearization-based computational algorithm of homotopy analysis method for nonlinear reaction–diffusion systems
URI https://dx.doi.org/10.1016/j.matcom.2021.11.027
Volume 194
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