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Stability analysis for fractional‐order partial differential equations by means of space spectral time Adams‐Bashforth Moulton method
Author(s) -
Sohail Ayesha,
Maqbool Khadija,
Ellahi Rahmat
Publication year - 2018
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22171
Subject(s) - linear multistep method , mathematics , convergence (economics) , spectral method , stability (learning theory) , partial differential equation , space (punctuation) , limiting , fractional calculus , mathematical analysis , partial derivative , differential equation , ordinary differential equation , computer science , differential algebraic equation , mechanical engineering , machine learning , economic growth , engineering , economics , operating system
In this article, a new numerical scheme space Spectral time Fractional Adam Bashforth Moulton method for the solution of fractional partial differential equations is offered. The proposed method is obtained by modifying, in a suitable way; the spectral technique and the method of lines. The attention is focused on the stability properties and hence an elegant stability analysis for the current approach is also provided. Finally, two examples are presented to illustrate the effectiveness of the reported method. Obtained results confirm the convergence and spectral accuracy of the proposed method in both space and time. In addition, a comparison with the existing studies is also made as a limiting case of the considered problem at the end and found in good agreement.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 34: 19–29, 2018