A Novel Approach with Time-Splitting Spectral Technique for the Coupled Schrdinger–Boussinesq Equations Involving Riesz Fractional Derivative

In the present paper the Riesz fractional coupled Schr¨odinger–Boussinesq(S-B) equations have been solved by the time-splitting Fourier spectral(TSFS) method. This proposed technique is utilized for discretizing the Schrdinger like equation and further, a pseudospectral discretization has been employed for the Boussinesq-like equation. Apart from that an implicit finite difference approach has also been proposed to compare the results with the solutions obtained from the time-splitting technique. Furthermore, the time-splitting method is proved to be unconditionally stable. The error norms along with the graphical solutions have also been presented here.