Implementation of the Tridiagonal Matrix Algorithm (TDMA) in C: A Practical Approach

Year : 2024 | Volume : 11 | Issue : 03 | Page : 36-43
    By

    Navya Jain,

  • Rishika Chauhan,

  • Pankaj Dumka,

  1. Student, Department of Computer Science and Engineering, Jaypee University of Engineering and Technology, Raghogarh-Vijaypur, Guan, Madhya Pradesh, India
  2. Assistant Professor, Department of Electronics and Communication Engineering, Jaypee University of Engineering and Technology, Raghogarh-Vijaypur, Guan, Madhya Pradesh, India
  3. Assistant Professor, Department of Mechanical Engineering, Jaypee University of Engineering and Technology, Raghogarh-Vijaypur, Guan, Madhya Pradesh, India

Abstract

This paper presents a practical implementation of the tridiagonal matrix algorithm (TDMA), also known as the Thomas algorithm, using the C programming language. The TDMA is a commonly used algorithm for solving systems of linear equations where the coefficient matrix is tridiagonal. The paper draws a detailed step-by-step process of the algorithm’s development, from forward elimination to backward substitution, with a focus on minimizing computational difficulty compared to standard Gaussian elimination. The simplicity and efficiency of TDMA make it an ideal choice in many engineering applications, such as structural analysis, heat conduction, and fluid dynamics, where large tridiagonal systems often arise. The C programming language is highlighted as a standard platform for implementing the TDMA due to its performance benefits, low-level memory management, and precision in handling numerical problems. The paper provides a comprehensive explanation of the algorithm’s core components, including vector initialization, solution printing, and the main TDMA solver function. Several practical examples were used to demonstrate the effectiveness of the implementation, validating the approach with commonly met tridiagonal systems in engineering scenarios. This study contributes to numerical analysis and engineering computation by offering a robust and efficient solution to tridiagonal systems. The implementation’s modularity and clear function structure also make it adaptable for educational and professional purposes, allowing for easy integration into more complex numerical simulations.

Keywords: TDMA, Thomas algorithm, C programming, tridiagonal matrix, numerical analysis

[This article belongs to Recent Trends in Programming languages ]

How to cite this article:
Navya Jain, Rishika Chauhan, Pankaj Dumka. Implementation of the Tridiagonal Matrix Algorithm (TDMA) in C: A Practical Approach. Recent Trends in Programming languages. 2024; 11(03):36-43.
How to cite this URL:
Navya Jain, Rishika Chauhan, Pankaj Dumka. Implementation of the Tridiagonal Matrix Algorithm (TDMA) in C: A Practical Approach. Recent Trends in Programming languages. 2024; 11(03):36-43. Available from: https://journals.stmjournals.com/rtpl/article=2024/view=180914


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Regular Issue Subscription Review Article
Volume 11
Issue 03
Received 09/10/2024
Accepted 14/10/2024
Published 04/11/2024
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