Abstract
This note presents a weak generalization of a time-delayed partial differential equation which, in turn, generalizes the well-known Burger–Fisher and Burgers–Huxley models. In this work, we provide a full discretization which is consistent with the integro-differential equation under consideration. The main analytical result of this note establishes that the discrete temporal rate of change of the discretization yields a consistent approximation to the differential form of the integro-differential equation investigated. Some numerical examples are provided in order to assess the efficiency and effectiveness of our methodology.
Acknowledgements
The author would like to thank the anonymous reviewers and the anonymous editor in charge of handling this manuscript for all their invaluable comments, suggestions and criticisms. He also wishes to acknowledge enlightening discussions with Dr José Villa-Morales, professor of the Department of Mathematics and Physics at the Universidad Autónoma de Aguascalientes.