Advanced Mathematical Models & Applications

ISSN Online: 2519-4445

Advanced Mathematical Models & Applications is a peer-reviewed, open access journal meant to publish original and significant results and articles in all areas of mathematical modeling and their applications. The aim of this Journal is to bring together researchers and practitioners from academia and industry to establishing new collaborations in this area. The Journal will consider for publication also review articles, literature reviews, correspondence concerning views and information published in previous issues.

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On Stability of Second-Order and Forth-Order Compact Finite Difference Methods for Solving Fuzzy Time Fractional Wave Equation in Double Parametric Form of Fuzzy Numbers

Published: 02-08-2026

https://doi.org/10.62476/amma112442

Abstract

In this paper, the stability of four finite difference methods—namely the Centre Time Centre Space (CTCS) method, the Crank-Nicolson method, the Compact Crank-Nicolson scheme, and the Compact Centre Time Centre Space (CCTCS) method—previously presented by the authors in earlier publications, is examined and analysed. The stability analysis of these schemes is conducted using the von Neumann (Fourier) method for the fuzzy time-fractional wave equation without a source term, expressed in the double-parametric form of a fuzzy number. The Caputo definition is used for the time-fractional derivative. The analysis reveals that the CTCS and CCTCS methods are conditionally stable, whereas the Crank-Nicolson and Compact Crank-Nicolson schemes are unconditionally stable.