A SEMI-ANALYTIC HYBRID APPROACH FOR SOLVING THE BUCKMASTER EQUATION
USING THE ELZAKI PROJECTED DIFFERENTIAL TRANSFORM METHOD (EPDTM)
Abstract
The Buckmaster equation, integral to the study of flat fluid plates and
their substantial deformation and dynamics, has long intrigued
researchers. Despite this, its complexity has confined solution attempts
to numerical methods, leaving a gap for an analytical approach.
Addressing this challenge, our study applies the Elzaki Projected
Differential Transform Method (EPDTM), which is a semi-analytic method,
to the nonlinear partial differential Buckmaster equation. This
innovative method stands out from previous numerical attempts with its
precision, efficiency, and minimal computational demand. Through the
EPDTM, we present approximate solutions for two specific cases and
extend our analysis to the general form of the Buckmaster equation.
Comparative visualizations against the exact solutions, supplemented by
tabular and graphical analyses, confirm the negligibility of absolute
errors. Crucially, convergence plots verify the EPDTM’s efficacy,
showcasing the solutions’ progressive alignment with the exact solution.
This study not only demonstrates the EPDTM’s potential in solving
complex equations with greater simplicity and speed but also opens
avenues for its application in broader mathematical and scientific
disciplines.