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Summary
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This study introduces a hybrid heuristic scheme using Log Sigmoid and Bernstein Polynomials to efficiently solve nonlinear heat transfer equations. The method optimizes parameters via Genetic Algorithm (GA) and Interior Point Algorithm (IPA), showing accurate results.

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Area of Science:

  • Numerical analysis
  • Heat transfer

Background:

  • Nonlinear heat transfer equations present significant challenges in finding accurate solutions.
  • Existing methods may lack efficiency or precision for complex nonlinear problems.

Purpose of the Study:

  • To develop and validate a novel hybrid heuristic scheme for efficiently solving nonlinear heat transfer equations.
  • To utilize Log Sigmoid and Bernstein Polynomial basis functions for formulating a trial solution.
  • To optimize unknown parameters using a combination of Genetic Algorithm (GA) and Interior Point Algorithm (IPA).

Main Methods:

  • A hybrid heuristic scheme integrating Genetic Algorithm (GA) and Interior Point Algorithm (IPA).
  • Transformation of nonlinear ordinary differential equations into a global error minimization problem.
  • Formulation of a trial solution using a fitness function with unknown parameters.

Main Results:

  • The proposed hybrid scheme effectively solves nonlinear heat transfer equations.
  • Results demonstrate sharp agreement with exact solutions and the Haar Wavelet-Quasilinearization technique.
  • Statistical analysis confirms the stability and reliability of the developed scheme.

Conclusions:

  • The hybrid GA-IPA scheme offers an effective and viable approach for solving nonlinear heat transfer problems.
  • The use of Log Sigmoid and Bernstein Polynomials contributes to the accuracy and efficiency of the method.
  • The validated scheme provides a robust tool for researchers in heat transfer analysis.