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A novel attempt for finding comparatively accurate solution for sine-Gordon equation comprising Riesz space fractional derivative. (English) Zbl 1416.65379

Summary: In this paper, a numerical procedure involving Chebyshev wavelet method has been implemented for computing the approximate solution of Riesz space fractional sine-Gordon equation (SGE). Two-dimensional Chebyshev wavelet method is implemented to calculate the numerical solution of space fractional SGE. The fractional SGE is considered as an interpolation between the classical SGE (corresponding to \(\alpha=2\)) and nonlocal SGE (corresponding to \(\alpha=1\)). As a consequence, the approximate solutions of fractional SGE obtained by using Chebyshev wavelet approach were compared with those derived by using modified homotopy analysis method with Fourier transform.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35R11 Fractional partial differential equations
35L71 Second-order semilinear hyperbolic equations
65T60 Numerical methods for wavelets
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