## THERMAL SCIENCE

International Scientific Journal

### 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.

**KEYWORDS**

PAPER SUBMITTED: 2018-08-24

PAPER REVISED: 2018-09-05

PAPER ACCEPTED: 2019-02-13

PUBLISHED ONLINE: 2019-05-26

**THERMAL SCIENCE** YEAR

**2019**, VOLUME

**23**, ISSUE

**3**, PAGES [1529 - 1537]

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