The Influence of Nonlinear Reaction, Memory and A Heaviside Function Source Term on Scalar Transport
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2016-06
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Addis Ababa University
Abstract
In this study, a numerical method based on finite difference is presented for the numerical solution of a generalized Fisher-Integro differential equation. A composite weighted trapezoidal rule is manipulated to handle the numerical integrations which results in a closed difference scheme. The non-linear terms are linearized by one of the finite difference linearization techniques. Three different methods are used; Left end point rule, right end point rule and trapezoidal end point rule. The numerical solutions obtained for the three methods indicate that, the approach is reliable and yields results compatible. The discretization of the governing equation is made by explicit, Implicit and Crank-Nicolson method time scheme.
The flow of an incompressible viscous fluid between a uniformly porous upper plate and a lower impermeable plate that is subjected to a FKPP is modeled and analyzed in this study. The Model equations are presented in terms of Left end point rule, Right end point rule and trapezoidal end point rule. For the Left end point rule, we are using the explicit method, for the right end point rule we are using the implicit method and for the trapezoidal end point rule we are using both implicit and explicit (Crank-Nicolson) method.
In this study, the researcher looked how to discretize integro-partial differential equation (memory term) using trapezoidal, left endpoints, right endpoints and Simpson’s rule. The literature highlights how the Fisher Kolomogrov-Petrovskii-Piskunov Equation is developed and used. The main part of this paper is dedicated in discretizing FKPP and developing a computer program to compute the solution.
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Computational