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Computational Analysis for Solving the Linear Space-Fractional Telegraph Equation

Open Journal of Modelling and Simulation 2022年第3期10卷 267-282页

作者： Zaki Mrzog Alaofi Talaat Sayed El-Danaf Adel Hadhoud Silvestru Sever Dragomir Department of Mathematics College of Science and Arts King Khalid University Muhayil Asir Saudi Arabia Mathematics College of Engineering & Science Victoria University Melbourne Australia Department of Mathematics Faculty of Sciences and Arts Taibah University Medina Saudi Arabia Department of Mathematics and Computer Science Faculty of Science Menoufia University Shebeen El-Kom Egypt

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.

关键词： Fractional Differential Equations quadratic spline functions Linear Space-Fractional Telegraph Equation Von Neumann Stability

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