Efficient Finite Difference Approaches for Solving Initial Boundary Value Problems in Helmholtz Partial Differential Equations

Authors

  • Bawar Mohammed Faraj Computer Science Department, College of Science, University of Halabja, Halabja, 46018, Iraq https://orcid.org/0000-0002-7543-2890
  • Shnyar Karim Rahman Department of Physics, College of Science, University of Halabja, Halabja, 46018, Iraq
  • Deni Adnan Mohammed Department of Physics, College of Science, University of Halabja, Halabja, 46018, Iraq
  • Hozan Dlshad Hilmi Department of Mathematics, College of Science, University of Sulaimani, Sulaimaniyah, 46001, Iraq
  • Ali Akgul Department of Electronics and Communication Engineering, Saveetha School of Engineering, SIMATS, Chennai, Tamil Nadu, India

DOI:

https://doi.org/10.37256/cm.4320232735

Keywords:

Helmholtz equation, initial boundary value problems (IBVP), finite difference scheme, computational techniques, stability analysis

Abstract

This study presents numerical solutions for initial boundary value problems of homogeneous and nonhomogeneous Helmholtz equations using first- and second-order difference schemes. The stability of these methods is rigorously analyzed, ensuring their reliability and convergence for a wide range of problem instances. The proposed schemes’ robustness and applicability are demonstrated through several examples, accompanied by an error analysis table and illustrative graphs that visually represent the accuracy of the solutions obtained. The results confirm the effectiveness and efficiency of the proposed schemes, making them valuable tools for solving Helmholtz equations in practical applications.

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Published

2023-09-07

How to Cite

1.
Faraj BM, Rahman SK, Mohammed DA, Hozan Dlshad Hilmi, Akgul A. Efficient Finite Difference Approaches for Solving Initial Boundary Value Problems in Helmholtz Partial Differential Equations. Contemp. Math. [Internet]. 2023 Sep. 7 [cited 2024 Mar. 4];4(3):569-80. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/2735

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