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SOLUTION OF FISHER’S EQUATION USING SUMUDU–ADOMIAN DECOMPOSITION METHOD.

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Title: SOLUTION OF FISHER’S EQUATION USING SUMUDU–ADOMIAN DECOMPOSITION METHOD.
Authors: AJANI, A. S.1, OLUBANWO, O. O.1, AYODELE, M. A.1, HARUNA, H. A.1, KAZEEM, Y. O.1, BECKLEY, A. O.1
Source: Annals of the Faculty of Engineering Hunedoara - International Journal of Engineering. Aug2026, Vol. 24 Issue 3, p145-152. 8p.
Subjects: Reaction-diffusion equations, Integral transforms, Scientific method, Fisher, Ronald Aylmer, Sir, 1890-1962, Theory of wave motion, Partial differential equations, Population dynamics
Abstract: This paper investigates the use of the Sumudu–Adomian Decomposition Method (SADM) to obtain approximate analytical solutions for Fisher’s Equation, a nonlinear partial differential equation that models reaction–diffusion processes such as population growth and gene propagation. The main purpose is to develop an efficient and accurate semi–analytical approach that overcomes the limitations of traditional numerical methods. The method combines the Sumudu Transform, which simplifies differential equations into algebraic expressions, with the Adomian Decomposition Method, which breaks down nonlinear terms into manageable components. This combination allows the nonlinear structure of Fisher’s Equation to be handled without linearisation or discretisation. The study outlines the procedural steps of SADM and demonstrates its effectiveness through several illustrative examples with different initial conditions. The results show that the series solutions obtained by SADM converge rapidly and accurately reproduce the expected wave–front behaviour of Fisher’s Equation. The approach significantly reduces computational effort while maintaining high precision. The findings confirm that SADM provides a simple, reliable, and efficient tool for solving nonlinear partial differential equations, making it suitable for a wide range of applications in science and engineering where nonlinear diffusion and growth phenomena are important. [ABSTRACT FROM AUTHOR]
Copyright of Annals of the Faculty of Engineering Hunedoara - International Journal of Engineering is the property of University Politehnica Timisoara, Faculty of Engineering Hunedoara 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: SOLUTION OF FISHER’S EQUATION USING SUMUDU–ADOMIAN DECOMPOSITION METHOD.
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  Data: <searchLink fieldCode="DE" term="%22Reaction-diffusion+equations%22">Reaction-diffusion equations</searchLink><br /><searchLink fieldCode="DE" term="%22Integral+transforms%22">Integral transforms</searchLink><br /><searchLink fieldCode="DE" term="%22Scientific+method%22">Scientific method</searchLink><br /><searchLink fieldCode="DE" term="%22Fisher%2C+Ronald+Aylmer%2C+Sir%2C+1890-1962%22">Fisher, Ronald Aylmer, Sir, 1890-1962</searchLink><br /><searchLink fieldCode="DE" term="%22Theory+of+wave+motion%22">Theory of wave motion</searchLink><br /><searchLink fieldCode="DE" term="%22Partial+differential+equations%22">Partial differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Population+dynamics%22">Population dynamics</searchLink>
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  Label: Abstract
  Group: Ab
  Data: This paper investigates the use of the Sumudu–Adomian Decomposition Method (SADM) to obtain approximate analytical solutions for Fisher’s Equation, a nonlinear partial differential equation that models reaction–diffusion processes such as population growth and gene propagation. The main purpose is to develop an efficient and accurate semi–analytical approach that overcomes the limitations of traditional numerical methods. The method combines the Sumudu Transform, which simplifies differential equations into algebraic expressions, with the Adomian Decomposition Method, which breaks down nonlinear terms into manageable components. This combination allows the nonlinear structure of Fisher’s Equation to be handled without linearisation or discretisation. The study outlines the procedural steps of SADM and demonstrates its effectiveness through several illustrative examples with different initial conditions. The results show that the series solutions obtained by SADM converge rapidly and accurately reproduce the expected wave–front behaviour of Fisher’s Equation. The approach significantly reduces computational effort while maintaining high precision. The findings confirm that SADM provides a simple, reliable, and efficient tool for solving nonlinear partial differential equations, making it suitable for a wide range of applications in science and engineering where nonlinear diffusion and growth phenomena are important. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
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  Data: <i>Copyright of Annals of the Faculty of Engineering Hunedoara - International Journal of Engineering is the property of University Politehnica Timisoara, Faculty of Engineering Hunedoara 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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        Text: English
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      – SubjectFull: Reaction-diffusion equations
        Type: general
      – SubjectFull: Integral transforms
        Type: general
      – SubjectFull: Scientific method
        Type: general
      – SubjectFull: Fisher, Ronald Aylmer, Sir, 1890-1962
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      – SubjectFull: Theory of wave motion
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      – SubjectFull: Partial differential equations
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      – SubjectFull: Population dynamics
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      – TitleFull: SOLUTION OF FISHER’S EQUATION USING SUMUDU–ADOMIAN DECOMPOSITION METHOD.
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              M: 08
              Text: Aug2026
              Type: published
              Y: 2026
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