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Accelerated nonstandard finite difference method for singularly perturbed Burger-Huxley equations.

Masho Jima Kabeto1, Gemechis File Duressa2

  • 1Department of Mathematics, Jimma University, Jimma, Ethiopia. maashookoo.reemii@gmail.com.

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|December 13, 2021
PubMed
Summary

This study introduces an accelerated nonstandard finite difference method to solve the singularly perturbed Burger-Huxley equation, achieving higher accuracy. The enhanced numerical technique improves convergence rates for more reliable computational results.

Keywords:
Accelerated nonstandard methodAccurate solutionSingularly perturbed Burger-Huxley equation

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Area of Science:

  • Computational Mathematics
  • Numerical Analysis
  • Partial Differential Equations

Background:

  • Singularly perturbed differential equations present challenges in numerical solutions.
  • The Burger-Huxley equation is a key model in various scientific domains.
  • Accurate numerical methods are crucial for understanding complex phenomena.

Purpose of the Study:

  • To develop an accelerated nonstandard finite difference method.
  • To enhance the accuracy of solutions for the singularly perturbed Burger-Huxley equation.
  • To improve the computational efficiency of existing numerical techniques.

Main Methods:

  • Linearization of the nonlinear term using quasilinearization.
  • Application of Mickens' nonstandard finite difference methodology in spatial and temporal directions.
  • Implementation of Richardson extrapolation to accelerate convergence from first to second-order.

Main Results:

  • A novel numerical method for the Burger-Huxley equation was successfully developed.
  • The accelerated method demonstrated improved accuracy compared to standard approaches.
  • Numerical experiments validated the theoretical findings and the effectiveness of the technique.

Conclusions:

  • The proposed accelerated nonstandard finite difference method is effective for solving the singularly perturbed Burger-Huxley equation.
  • The combination of quasilinearization, Mickens' method, and Richardson extrapolation yields accurate and efficient solutions.
  • This approach offers a valuable tool for researchers dealing with similar differential equations.