The basic aim of this paper is to introduce
and describe an efficient numerical scheme based on spectral approach coupled
with Chebyshev wavelets for the approximate solutions of Klein-Gordon and
Sine-Gordon equations. The main characteristic is that, it converts the given
problem into a system of algebraic equations that can be solved easily with any
of the usual methods. To show the accuracy and the efficiency of the method,
several benchmark problems are implemented and the comparisons are given with other
methods existing in the recent literature. The results of numerical tests confirm
that the proposed method is superior to other existing ones and is highly
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