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An Advanced Galerkin Approach to Solve the Nonlinear \\[6pt]Reaction-Diffusion Equations With Different Boundary Conditions

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Listed:
  • Hazrat Ali
  • Md. Kamrujjaman
  • Md. Shafiqul Islam

Abstract

This study proposed a scheme originated from the Galerkin finite element method (GFEM) for solving nonlinear parabolic partial differential equations (PDEs) numerically with initial and different types of boundary conditions. The scheme is applied generally handling the nonlinear terms in a simple way and throwing over restrictive assumptions. The convergence and stability analysis of the method are derived. The error of the method is estimated. In the series, eminent problems are solved, such as Fisher's equation, Newell-Whitehead-Segel equation, Burger's equation, and Burgers-Huxley equation to demonstrate the validity, efficiency, accuracy, simplicity and applicability of this scheme. In each example, the comparison results are presented both numerically and graphically

Suggested Citation

  • Hazrat Ali & Md. Kamrujjaman & Md. Shafiqul Islam, 2022. "An Advanced Galerkin Approach to Solve the Nonlinear \\[6pt]Reaction-Diffusion Equations With Different Boundary Conditions," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 14(1), pages 1-30, March.
    • Handle: RePEc:ibn:jmrjnl:v:14:y:2022:i:1:p:30
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    References listed on IDEAS

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    1. Hazrat Ali & Md Kamrujjaman & Md Shafiqul Islam, 2020. "Numerical Computation of Fitzhugh-Nagumo Equation: A Novel Galerkin Finite Element Approach," International Journal of Mathematical Research, Conscientia Beam, vol. 9(1), pages 20-27.
    2. Sapa, Lucjan, 2018. "Difference methods for parabolic equations with Robin condition," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 794-811.
    3. Md. Hazrat Ali & Md. Md. Kamrujjaman & Md. Md. Shafiqul Islam, . "Numerical Computation of Fitzhugh-Nagumo Equation: A Novel Galerkin Finite Element Approach," International Journal of Mathematics Research, Conscientia Beam, pages 20-27.
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      JEL classification:

      • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
      • Z0 - Other Special Topics - - General

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