Abstract
In this work, we have considered a Sharma–Tasso–Olver (STO) equation in order to obtain some exact and numerical solutions by using the auto-Backlund transformation method (aBTM) and the finite forward difference method. We successfully obtain some kink-type solutions with exponential prototype structure to this equation and also we obtain some numerical solution by using the finite difference method (FDM). We illustrate the comparison between exact and numerical approximations and support the comparison with a graphic plot of these illustrations as well. Moreover, the Fourier–von Neumann stability analysis is used in checking the stability of the numerical scheme. The L2 and L∞ error norms of the solutions to this equation are also illustrated here.
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