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In this article, non-linear Equal Width-Wave (EW) equation will benumerically solved . For this aim, the non-linear term in the equation isfirstly linearized by Rubin-Graves type approach. After that, to reduce theequation into a solvable discretized linear algebraic equation system which isthe essential part of this study, the Crank-Nicolson type approximation andcubic Hermite collocation method are respectively applied to obtain theintegration in the temporal and spatial domain directions. To be able toillustrate the validity and accuracy of the proposed method, six test modelproblems that is single solitary wave, the interaction of two solitary waves,the interaction of three solitary waves, the Maxwellian initial condition,undular bore and finally soliton collision will be taken into consideration andsolved. Since only the single solitary wave has an analytical solution amongthese solitary waves, the error norms Linf and L2 are computed and compared toa few of the previous works available in the literature. Furthermore, thewidely used three invariants I1, I2 and I3 of the proposed problems during thesimulations are computed and presented. Beside those, the relative changes inthose invariants are presented. Also, a comparison of the error norms Linf andL2 and these invariants obviously shows that the proposed scheme producesbetter and compatible results than most of the previous works using the sameparameters. Finally, von Neumann analysis has shown that the present scheme isunconditionally stable.

A Powerful Robust Cubic Hermite Collocation Method for the Numerical Calculations and Simulations of the Equal Width Wave Equation