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The ultimate goal and highlight of this paper are to explore water levels along the coast of Bangladesh efficiently due to the nonlinear interaction of tide and surge by employing the method of lines (MOLs) with the aid of newly proposed RKAHeM(4,4) technique.In this regard,the spatial derivatives of shallow water equations (SWEs) were discretized by means of a finite difference method to obtain a system of ordinary differential equations (ODEs) of initial valued with time as an independent variable.The obtained system of ODEs was solved by the RKAHeM(4,4)technique.One-way nested grid technique was exercised to incorporate coastal complexities closely with minimum computational cost.A stable tidal oscillation was produced over the region of interest by applying the most influential tidal constituent M2 along the south open boundary of the outer scheme.The newly developed model was applied to estimate water levels due to the non-linear interaction of tide and surge associated with the catastrophic cyclone April 1991 along the coast of Bangladesh.The approach employed in the study was found to perform well and ensure conformity with real-time observations.