A solitary wave solution to the generalized Burgers-Fisher's equation using an improved differential transform method: A hybrid scheme approach

Abstract

In this research, an unrivalled hybrid scheme which involves the coupling of the new Elzaki integral transform (an improved version of Laplace transform) and a modified differential transform called the projected differential transform (PDTM) have been implemented to solve the generalized Burgers-Fisher's equation; which springs up due to the fusion of the Burgers' and the Fisher's equation; describing convective effects, diffusion transport or interaction between reaction mechanisms, traffic flows; and turbulence; consequently finding meaningful applicability in the applied sciences viz: gas dynamics, fluid dynamics, turbulence theory, reaction-diffusion theory, shock-wave formation, traffic flows, financial mathematics, and so on. Using the proposed Elzaki projected differential transform method (EPDTM), a generalized exact solution (Solitary solution) in form of a Taylor multivariate series has been obtained; of which the highly nonlinear terms and derivatives handled by PDTM have been decomposed without expansion, computation of Adomian or He's polynomials, discretization, restriction of parameters, and with less computational work whilst achieving a highly convergent results when compared to other existing analytical/exact methods in the literature, via comparison tables, 3D plots, convergence plots and fluid-like plots. Thus showing the distinction, novelty and huge advantage of the proposed method as an asymptotic alternative, in providing generalized or solitary wave solution to a wider class of differential equations.

Noval soliton solution, sensitivity and stability analysis to the fractional gKdV-ZK equation

“…Recently many powerful techniques for attaining the exact solution of NPDEs have been presented, such as Jacobi-elliptic approach 7 , Sine-Gordon expansion scheme 8 – 10 , modified simple equation scheme 11 , the Kudryashov approach 12 , auxiliary equation technique 13 , 14 , Exp-function method 15 , the extended direct algebraic method 16 – 19 , -expansion method 17 , 20 , extended tanh expansion scheme 21 , -expansion method 22 , Hirota bilinear method 23 , 24 , modified rational expansion method 25 , modified Sardar sub-equation method 26 , the Riccati equation mapping method 27 , F-expansion method 28 and many more 29 – 33 .…”

A Hybrid Non-Polynomial Spline Method and Conformable Fractional Continuity Equation

“…Solving this equation presents a formidable challenge due to its nonlinear and non-local characteristics. In response to this challenge, numerous numerical methodologies have been proposed in the existing literature, which include the cubic B-spline method [47], the finite element method [48], the recently enhanced differential transform method [49], and the Hermite spline collection method [50]. However, In the realm of mathematical modeling and scientific computation, the application of various techniques has proven to be indispensable.…”

Modelling the impact of some control strategies on the transmission dynamics of Ebola virus in human-bat population: An optimal control analysis

“…The virus spreads via direct contact with the body of fluidic outputs (urine, breast milk, feces, semen, vomit, amniotic fluid, sweat, saliva) of Ebola patients or the deceased body of Ebola patients, contaminated objects, infected fruits bats, or nonhuman primates which includes apes and monkeys, semen from a man who recovered from Ebola virus. And through the two treatment (Inmazeb and Ebanga) which was approved by the U.S. Food and Drug Administration (FDA) and Supportive Care, the endemic and epidemic status of Ebola virus disease in the milieu are increasingly curbed [38] , [49] . Implementing methods like supportive management, isolation, and quarantine of the infected individuals in the affected geographical area, the dynamic transmission was curtailed and the case fatality rate (CFR) was kept at 40% as 8 out of the 20 infected humans yielded to the virus including a considerable number of health practitioners.…”