Comparative Study of Fractional and Integer-Order Telegraph Equations: Numerical Methods and Stability Analysis
Keywords:
Time-fractional telegraph equation, Caputo derivative, finite difference method, numerical stability, accuracy comparisonAbstract
This study investigates the numerical solutions of the time-fractional telegraph equation formulated using the Caputo derivative. Employing both first-order and second-order finite difference schemes, we establish stable discretization methods to approximate the solution of the equation. Theoretical stability analyses are presented for each scheme. To assess the accuracy and performance of the methods, we conduct numerical experiments comparing the results of the fractional-order model with those of the classical integer-order case. The comparison demonstrates that the second-order scheme yields superior accuracy over the first-order scheme, and that the fractional-order formulation offers improved approximations compared to its classical counterpart. The analytical and numerical solutions are graphically illustrated using MATLAB, confirming the reliability and efficiency of the proposed methods.
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Copyright (c) 2026 Mahmut Modanli, Fatih Ozbag
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