| Summary: | This paper examines the effects of three distinct numerical schemes (Adomian Decomposition, quintic & septic Spline methods) to investigate semi-analytical and approximate solutions on Wu–Zhang (ZW) system. It describes the (1+1)-dimensional dispersive long wave in two horizontal directions on shallow waters. The ZW model is one of the fractional nonlinear partial differential equations. Conformable derivatives properties are employed to convert the nonlinear fractional partial differential equation into an ordinary differential equation with integer order so as to obtain the approximate solutions for this model. The solutions obtained for each technique were compared to reveal their relationship to their characteristics illustrated under the suitable choice of the parameters values. The obtained solutions showed the power, easiness, and effectiveness of these methods on nonlinear partial differential equations. Keywords: Fractional nonlinear Wu–Zhang system, Conformable fractional derivatives, Numerical schemes
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