Document Type : Research Paper

Authors

• Mathew O. Aibinu ^{1, 2}
• S. Moyo ^{3, 4}

¹ Institute for Systems Science and KZN e-Skills CoLab, Durban University of Technology, South Africa

² DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), South Africa

³ Department of Applied Mathematics and School for Data Science and Computational Thinking, Stellenbosch University, South Africa

⁴ National Institute for Theoretical and Computational Sciences (NITheCS), South Africa

Abstract

Many generalizations have been considered on how to construct the exact solutions of one-component Reaction-Diffusion (RD) equations. Two-component RD systems of equations allow for the study of a wider range of physical phenomena as well as dynamical processes than their counterpart one-component RD equations. The most suitable and best way to study certain models is by using two-component RD systems of equations. Moreover, the presence of delay in nonlinear Partial Differential Equations (PDEs) makes them more difficult to study than those without delay. This study introduces some new exact solutions associated with a generalized form of two-component RD systems of equations with delay. The exact solutions for more complex multidimensional reaction-diffusion systems of equations are also derived. Solutions to RD systems of equations with a delay which are presented in this study are applicable for the formulation of test problems to verify the efficiency of numerical methods which are being used to obtain the solutions of nonlinear delay PDEs.

Keywords

• Reaction-diffusion
• Exact solutions
• Delay differential equations
• Fundamental matrix
• Systems of equations