A B-spline is defined by the degree and quantity of knots, and it is observed to provide a
higher level of flexibility in curve and surface layout. The extended cubic B-spline (ExCBS) …

In this paper, the examination of soliton solutions of the biofilm model with the help of a new
extended direct algebraic method is expressed. Besides the exact solutions, the existence of …

The investigation presented in this study delves into the analysis of Lie symmetries for the
bistable Allen-Cahn (BAC) equation with a quartic potential, specifically applied to the …

Heat transfer processes in a photovoltaic (PV) silicon solar panel are simulated under
standard circumstances. A model containing an intricate treatment of the incoming solar …

Two standard and two nonstandard finite difference schemes are constructed to solve a
basic reaction–diffusion–chemotaxis model, for which no exact solution is known. The …

Introduction Fractional diffusion equations offer an effective means of describing transport
phenomena exhibiting abnormal diffusion pat-terns, often eluding traditional diffusion …

The main aim of this article is to propose a general framework for the theoretical analysis of
discrete schemes used to solve multi-dimensional parabolic problems with fractional power …

This study introduces the higher-order unconditionally positive finite difference (HUPFD)
methods to solve the linear, nonlinear, and system of advection–diffusion–reaction (ADR) …

One standard and two nonstandard finite difference methods are used to solve a convective
predator-prey model consisting of cross-diffusion terms for which no exact solution is known …

The keys to constructing numerical schemes for nonlinear partial differential equations are
accuracy, handling of the nonlinear terms, and physical properties (energy dissipation or …