International Journal of Numerical Methods and Applications

The International Journal of Numerical Methods and Applications publishes research articles on numerical methods and their applications in various fields, including differential equations, fluid dynamics, and bioinformatics. It also welcomes survey articles on new methods in numerical analysis.

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EXPLICIT FORMULA FOR THE CLASSICAL SOLUTION OF THE CAUCHY PROBLEM FOR THE TELEGRAPH EQUATION WITH DIRAC POTENTIAL

Authors

  • TOGNEME Alowou-Egnim
  • KAMAN Mondobozi Lélén
  • SAMIE Dawaïdom

Keywords:

Cauchy problem, telegraph equation, Dirac potential, Duhamel principle, d’Alembert formula, classical solution

DOI:

https://doi.org/10.17654/0975045225019

Abstract

We have established the classical solution for the Cauchy problem for the telegraph equation with Dirac potential, whose free term is of the form $\gamma u\left(x_0, t_0\right)$, where $u(x, t)$ is the function sought at the point $\left(x_0, t_0\right)$ using Duhamel's principle and d'Alembert's formula.

Received: May 6, 2025
Revised: June 9, 2025
Accepted: June 11, 2025

References

[1] E. I. Moiseev and N. I. Yurchuk, Classical and generalized solutions of problems for the telegraph equation with a Dirac potential, Differential Equations 51(10) (2015), 1330-1337.

[2] M. T. Dzhenaliev, On loaded equations with periodic boundary conditions, Differ. Uravn. 37(1) (2001), 48-54.

[3] M. T. Dzhenaliev and M. I. Ramazanov, On a boundary value problem for a spectrally loaded heat operator I, Differ. Uravn. 43(4) 2007, 498-508.

[4] A.-E. Togneme, M. L. Kaman, P. K. Siliadin and K. Tcharie, On the existence and uniqueness of classical and strong generalized solutions of Cauchy problem for the Euler-Poisson-Darboux equation with a Dirac potential, Far East Journal of Mathematical Sciences (FJMS) 119(2) (2019), 167-176.

[5] A. E. Togneme, M. L. Kaman, P. K. Siliadin and K. Tcharie, Problème de Cauchy pour une equation d’Euler-Poisson-Darboux avec potentiel de Dirac, Anales Mathématiques Africaines 8 (2020), 91-96.

[6] A. I. Kozhanov, On nonlinear loaded parabolic equation and a related inverse problem, Mat. Zametki 76(6) (2004), 84-91.

[7] M. T. Dzhenaliev and M. I. Ramazanov, On a boundary value problem for a spectrally loaded heat operator II, Differ. Uravn. 43(6) 2007, 788-794.

[8] O. Thual, Solutions de l’équation de d’Alembert, Fiche de cours, chapitre 3, 2021.

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Published

2025-09-02

Issue

Vol. 25 No. 2 (2025)

Section

Articles

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How to Cite

EXPLICIT FORMULA FOR THE CLASSICAL SOLUTION OF THE CAUCHY PROBLEM FOR THE TELEGRAPH EQUATION WITH DIRAC POTENTIAL. (2025). International Journal of Numerical Methods and Applications, 25(2), 457-466. https://doi.org/10.17654/0975045225019

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