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An innovative subdivision collocation algorithm for heat conduction equation with non-uniform thermal diffusivity.

Syeda Tehmina Ejaz1, Safia Malik2, Jihad Younis3

  • 1Department of Mathematics, The Government Sadiq College Women University, Bahawalpur, 63100, Pakistan. syedatehmina.ejaz@gscwu.edu.pk.

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Summary
This summary is machine-generated.

A new subdivision collocation algorithm accurately solves the heat conduction equation with varying thermal diffusivity. This numerical method enhances precision compared to existing approaches for heat transfer problems.

Keywords:
Collocation methodErrorHeat conduction equationPartial differential equationStabilitySubdivision scheme

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Area of Science:

  • Numerical Analysis
  • Heat Transfer

Background:

  • Accurate numerical solutions are crucial for understanding heat conduction phenomena.
  • Non-uniform thermal diffusivity presents significant challenges in traditional modeling.
  • Existing numerical methods may lack sufficient accuracy for complex thermal scenarios.

Purpose of the Study:

  • To introduce a novel subdivision collocation algorithm for solving the heat conduction equation.
  • To address the complexities introduced by non-uniform thermal diffusivity.
  • To verify and demonstrate the superior accuracy of the proposed numerical method.

Main Methods:

  • The subdivision collocation algorithm transforms the heat conduction equation into a system of equations.
  • Discretization of the time variable is performed using the finite difference formula.
  • The algorithm's feasibility is confirmed through theoretical analysis and numerical simulations.

Main Results:

  • The proposed algorithm successfully obtains numerical solutions for the heat conduction equation.
  • Theoretical and numerical analyses validate the algorithm's feasibility.
  • Comparisons with existing methods show the proposed algorithm achieves higher accuracy.

Conclusions:

  • The subdivision collocation algorithm provides an accurate and effective approach for solving heat conduction problems with non-uniform thermal diffusivity.
  • The method demonstrates superior performance over existing techniques.
  • The findings offer a valuable tool for advanced heat transfer analysis.