A Solutions of the Linearized Two-Dimensional Generalized Dispersive Wave Equation with Mixed Derivative via the Residual Power Series Method

Abstract

This article applies the Residual Power Series Method (RPSM) to solve the Linearized Two-Dimensional Generalized Dispersive Wave Equation (L-2DGDWE) featuring the mixed derivative term $u_{xt}$. The RPSM is based on the general Taylor series formula combined with a residual error function minimization. A new analytical solution is investigated in this work. The analytical solution is designed to find approximate solutions via RPSM, and these obtained results are compared with exact solutions to demonstrate the precision, reliability, and rapid convergence of the proposed method. Graphical representations at different time instances are provided to visualize the solution behavior.