Efficient numerical analysis of nonlinear liquid dispersion pattern drops using Taylor wavelet collocation

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In this article, the Taylor wavelet collocation method (TWCM) is presented for solving the nonlinear Rosenau-Hyman equation, which models nonlinear dispersion in liquid drop formation. TWCM outperforms existing methods, such as the Hermite wavelet and other semi-analytical approaches, by providing higher computational efficiency and accuracy. The differential equation is converted into a system of algebraic equations, solved using the Broyden-Quasi Newton algorithm. Numerical examples demonstrate the reliability and robustness of TWCM in handling nonlinear dispersion patterns. All calculations and visualizations are performed using Matlab, showcasing the method's effectiveness and advancement in analyzing nonlinear liquid dispersion.

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