Computational Analysis for Solving the Linear Space-Fractional Telegraph Equation - Open Journal of Modelling and Simulation

OJMSi > Vol.10 No.3, July 2022

Open Journal of Modelling and Simulation

Volume 10, Issue 3 (July 2022)

ISSN Print: 2327-4018 ISSN Online: 2327-4026

Google-based Impact Factor: 2.79 Citations

Computational Analysis for Solving the Linear Space-Fractional Telegraph Equation ()

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DOI: 10.4236/ojmsi.2022.103014 172 Downloads 772 Views Citations

Author(s)

Zaki Mrzog Alaofi^1,2, Talaat Sayed El-Danaf³, Adel Hadhoud⁴, Silvestru Sever Dragomir²

Affiliation(s)

¹Department of Mathematics, College of Science and Arts, King Khalid University, Muhayil Asir, Saudi Arabia.
²Mathematics, College of Engineering & Science, Victoria University, Melbourne, Australia.
³Department of Mathematics, Faculty of Sciences and Arts, Taibah University, Medina, Saudi Arabia.
⁴Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shebeen El-Kom, Egypt.

ABSTRACT

Over the last few years, there has been a significant increase in attention paid to fractional differential equations, given their wide array of applications in the fields of physics and engineering. The recent development of using fractional telegraph equations as models in some fields (e.g., the thermal diffusion in fractal media) has heightened the importance of examining the method of solutions for such equations (both approximate and analytic). The present work is designed to serve as a valuable contribution to work in this field. The key objective of this work is to propose a general framework that can be used to guide quadratic spline functions in order to create a numerical method for obtaining an approximation solution using the linear space-fractional telegraph equation. Additionally, the Von Neumann method was employed to measure the stability of the analytical scheme, which showed that the proposed method is conditionally stable. What’s more, the proposal contains a numerical example that illustrates how the proposed method can be implemented practically, whilst the error estimates and numerical stability results are discussed in depth. The findings indicate that the proposed model is highly effective, convenient and accurate for solving the relevant problems and is suitable for use with approximate solutions acquired through the two-dimensional differential transform method that has been developed for linear partial differential equations with space- and time-fractional derivatives.

KEYWORDS

Fractional Differential Equations, Quadratic Spline Functions, Linear Space-Fractional Telegraph Equation, Von Neumann Stability

Share and Cite:

Alaofi, Z. , El-Danaf, T. , Hadhoud, A. and Dragomir, S. (2022) Computational Analysis for Solving the Linear Space-Fractional Telegraph Equation. Open Journal of Modelling and Simulation, 10, 267-282. doi: 10.4236/ojmsi.2022.103014.

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