An improved differential transform scheme implementation on the generalized Allen–Cahn equation governing oil pollution dynamics in oceanography
Kingsley Timilehin Akinfe, Adedapo Chris Loyinmi
Abstract
Studies in computational mathematics have taken a fantastic aesthetics in interdisciplinary fields as researchers in this area have resiliently adopted constructive methods, schemes, algorithms, and techniques on the nonlinear differential equations, to succinctly analyze the dynamical behavior of established models for which this study has yet, coupled the Elzaki integral transform as a before treatment to complement domain decomposition for increased accuracy and convergence with the projected differential transform method, yielding an improved differential transform technique (EPDTM), on a cogent extract of the generalized oil pollution and spillage’s governing equation viz: the Allen–Cahn equation which describes oil pollution dynamics, reaction–diffusion mechanisms, and mechanics of crystalline solids with an interfacial thickness parameter ɛ, with applications in solid-state physics, imaging, plasma physics, material science and so on, for which material and plasma sciences may benefit from these solutions. The validatory analysis of this hybrid technique via tables, graphical illustrations with arbitrarily varied parameters, and convergence analysis ascertained the consistency, uniqueness, and convergence of our obtained analytical results, thus, distinct from existing works of the literature. Notably, the dynamical scrutiny carried out utilizing the developed EPDTM solution revealed an increase in the model’s periodicity with a constant wavelength for each increase in the interfacial thickness parameter ɛ, which is realistically valid for the Allen–Cahn model.