Advanced Transform Techniques for the One-Dimensional Non-Homogeneous Heat Equation with Non-Homogeneous BCs and IC

Authors

  • RAPHEAL OLADIPO FIFELOLA

    DEPARTMENT OF MATHEMATICAL SCIENCES, FACULTY OF SCIENCE, NIGERIAN DEFENCE ACADEMY

  • OKAFOR UCHENWA LINUS

    DEPARTMENT OF MATHEMATICAL SCIENCES, FACULTY OF SCIENCES, NIGERIAN DEFENCE ACADEMY.

  • ADEDAPO KEHINDE FEMI

    DEPARTMENT OF PHYSICAL AND CHEMICAL SCIENCES,FEDERAL UNIVERSITY OF HEALTH SCIENCES

  • JOHNSON SUNDAY EGBEJA

    DEPARTMENT OF MATHEMATICAL SCIENCES, FACULTY OF SCIENCES, NIGERIAN DEFENCE ACADEMY.

How to Cite

FIFELOLA, R. O., OKAFOR UCHENWA LINUS, ADEDAPO KEHINDE FEMI, & JOHNSON SUNDAY EGBEJA. (2024). Advanced Transform Techniques for the One-Dimensional Non-Homogeneous Heat Equation with Non-Homogeneous BCs and IC. International Journal of Applied Mathematical Research, 13(2), 96-102. https://doi.org/10.14419/kyyb9f56

Received date: August 6, 2024

Accepted date: August 31, 2024

Published date: September 22, 2024

DOI:

https://doi.org/10.14419/kyyb9f56

Keywords:

Heat Equation, Boundary Conditions, Fourier Series, Non-Homogeneous PDE, Transformation Method.

Abstract

This study addresses the one-dimensional non-homogeneous heat equation with non-homogeneous boundary conditions using a transformation method. We introduce a new dependent variable V(x,t) and a function ψ(x) to simplify the PDE into a homogeneous form, solving it analytically. The solution involves separating variables and applying Fourier series, leading to:

Numerical simulations confirm the theoretical results, illustrating the method’s robustness for modeling heat conduction problems.

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How to Cite

FIFELOLA, R. O., OKAFOR UCHENWA LINUS, ADEDAPO KEHINDE FEMI, & JOHNSON SUNDAY EGBEJA. (2024). Advanced Transform Techniques for the One-Dimensional Non-Homogeneous Heat Equation with Non-Homogeneous BCs and IC. International Journal of Applied Mathematical Research, 13(2), 96-102. https://doi.org/10.14419/kyyb9f56

Received date: August 6, 2024

Accepted date: August 31, 2024

Published date: September 22, 2024