THEORETICAL FOUNDATIONS AND SPECIFICITY OF MATHEMATICAL MODELLING

Application of Sturm Liouville Problem in the Wave Equation

  • 1 Polytechnic University of Tirana, Albania

Abstract

Partial differential equations (PDEs) are differential equations in which there is more than one independent variable. They arise in the modelling of a wide-range of physical phenomena including electromagnetism, fluid flow, elasticity, quantum mechanics and heat conduction. The wave equation serves as a fundamental model for understanding various wave phenomena in physics and engineering. In this paper, we explore the application of Sturm-Liouville problems to solve the wave equation. The results of our investigations not only showcase the accuracy and computational advantages of the Sturm-Liouville method but also shed light on the physical interpretations of the obtained eigenfunctions and eigenvalues. In conclusion, this paper contributes to the body of knowledge regarding the application of SturmLiouville problems in wave equation modeling and analysis. It offers a valuable perspective for researchers, scientists, and engineers seeking efficient and insightful solutions to wave-related challenges. The versatility and effectiveness of the Sturm-Liouville approach make it a compelling tool for gaining deeper insights into wave phenomena and their practical applications.

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References

  1. W. O. Amrein, A. M. Hinz, D. B. Pearson, “Sturm-Liouville Theory, Past and Present”, BIRKHÄUSER, ISBN-10: 3-7643- 7066-1, (2005).
  2. M.A. Al-Gwaiz, “Sturm-Liouville Theory and its Applications”, SPRINGER, ISBN 978-1-84628-971-2, (2008)
  3. E. Kreyszig, H. Kreyszig, E. J. Norminton, “Advanced Engineering Mathematics”, WILEY, ISBN 978-0-470-45836- 5, (2011)
  4. K. A. Stroud, “Advanced Engineering Mathemarics”, PALGRAVE MACMILLAN, ISBN 978-1-4039-0312-9, (2003)
  5. R. B. Guenther, J. W. Lee, “Sturm-Liouville Problems Theory and Numerical Implementation”, CRC PRESS, ISBN 9781138345430, (2019)
  6. L. Gjoka, and A. Daci. "Analiza C," Ekuacione Diferenciale, Sisteme Dinamike." (2019).

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