Qualitative Study on Finite Volume Method for Solving Linear and Nonlinear Partial Differential Equations

Authors

  • Abdulkafi Mohammed Saeed Department of Mathematics, College of Science, Qassim University, Buraydah, Kingdom of Saudi Arabia https://orcid.org/0000-0001-9560-105X
  • Thekra Abdullah Alfawaz Department of Mathematics, College of Science, Qassim University, Buraydah, Kingdom of Saudi Arabia

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i2.5892

Keywords:

linear advection equation, nonlinear Burgers' equation, finite volume method, computational fluid dynamics, Errors Analysis

Abstract

Numerous numerical solutions have been developed over the past decades to provide suitable solutions for several types of problems in computational fluid dynamics (CFD). The finite volume method (FVM) is a numerical technique adopted in computational fluid dynamics to solve partial differential equations representing conservation laws. In this article, two mathematical models are presented: one for the linear advection equation and another for the nonlinear Burgers' equation with diffusion, along with various schemes of the FVM. Furthermore, numerical experiments will be conducted for several FVM schemes to demonstrate the most effective approach for solving the studied problem.

Author Biography

  • Thekra Abdullah Alfawaz, Department of Mathematics, College of Science, Qassim University, Buraydah, Kingdom of Saudi Arabia
    Department of Mathematics, College of Science

Downloads

Published

2025-05-01

Issue

Vol. 18 No. 2: (April 2025)

Section

Differential Equations

License

Copyright (c) 2025 Abdulkafi Mohammed Saeed, Thekra Abdullah Alfawaz

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.

By agreeing to this statement, you acknowledge that:

  • You retain full copyright over your work.
  • The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
  • This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.

How to Cite

Qualitative Study on Finite Volume Method for Solving Linear and Nonlinear Partial Differential Equations. (2025). European Journal of Pure and Applied Mathematics, 18(2), 5892. https://doi.org/10.29020/nybg.ejpam.v18i2.5892