Abstract
In this research, we proposed the fusing of Elzaki transform and projected differential transform (PDTM) to obtain an analytical or approximate solution of the Rosenau-Hyman and Korteweg-de Vries equations which respectively govern pattern formation in liquid drops and model of waves on shallow water surfaces. The results obtained presented in tables and graphs showed better efficiency, accuracy, and convergence of the method to handle Rosenau-Hyman and Korteweg-de Vries equations when compared to other methods in the literature.
 Keywords: Rosenau-Hyman Equation; Korteweg-de Vries equation; Elzaki Projected differential transform method; Semi-analytic approach
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