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THE NUMERICAL SOLUTION OF THE TIME-FRACTIONAL NON-LINEAR KLEIN-GORDON EQUATION VIA SPECTRAL COLLOCATION METHOD

ABSTRACT
In this paper, we consider the numerical solution of the time-fractional non-linear Klein-Gordon equation. We propose a spectral collocation method in both temporal and spatial discretizations with a spectral expansion of Jacobi interpolation polynomial for this equation. A rigorous error analysis is provided for the spectral methods to show both the errors of approximate solutions and the errors of approximate derivatives of the solutions decaying exponentially in infinity-norm and weighted L2-norm. Numerical tests are carried out to confirm the theoretical results.
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PAPER SUBMITTED: 2018-08-24
PAPER REVISED: 2018-09-05
PAPER ACCEPTED: 2019-02-13
PUBLISHED ONLINE: 2019-05-26
DOI REFERENCE: https://doi.org/10.2298/TSCI180824220Y
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE 3, PAGES [1529 - 1537]
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© 2019 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence