Exact solutions to the family of Fisher's reaction‐diffusion equation using Elzaki homotopy transformation perturbation method

• Published in: Engineering reports (Hoboken, N.J.) N.J.), 2020-02, Vol.2 (2), p.n/a
• Main Authors: Loyinmi, Adedapo C., Akinfe, Timilehin K.
• Format: Article
• Language: English
• Subjects: 3D plots; convergence plots; Elzaki transform; genetic propagation; genetic theory; homotopy perturbation; multivariate series; nonlinear partial differential equations; reaction‐diffusion equations; table of comparison exact results
• ISSN: 2577-8196; 2577-8196
• DOI: 10.1002/eng2.12084

In this research work, we propose an unprecedented hybrid algorithm which involves the coupling of a new integral transform, namely, the Elzaki transform and the well‐known homotopy perturbation method called the Elzaki homotopy transformation perturbation method (EHTPM) to solve for the exact solution of three distinct types of Fisher's equation, namely, the Fisher's equation of two cases, the sixth‐order Fisher's equation and the nonlinear diffusion equation of the Fisher type. These equations are prominent in mathematical biology and highly applicable in genetic propagation, population dynamics, stochastic processes, combustion theory, as well as a prototype model for a spreading flame, and so on. The efficacy and authenticity of this method was established via convergence and error analysis, and shows that the solutions obtained from EHTPM are unique and convergent. The results of EHTPM when compared with the exact results, homotopy results, and results from the other existing literature via table of comparison, 3D plots, and the convergence plots validates that EHTPM is an efficient and reliable tool of providing exact solutions to a wider class of nonlinear partial differential equations in a simple and straightforward manner, with no discretization, linearization, computation of Adomian polynomials, and devoid of errors. We have considered a prominent Nonlinear partial differential equation which governs the spatial spread and propagation of mutant genes. A new integral transform called the Elzaki transform was coupled with Homotopy perturbation to solve for the exact solution of this model. The results when compared with existing methods agreed well and shows a high level of convergence.