A new analysis of a partial differential equation arising in biology and population genetics via semi analytical techniques
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Date
2020
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Abstract
In this work, we propose a new optimal perturbation iteration method for solving the generalized Fitzhugh–Nagumo equation with time-dependent coefficients. This research reveals that the new proposed technique, with the aid of symbolic computations, provides a straightforward and impressive mathematical tool for solving nonlinear partial differential equations. Implementing this method to Fitzhugh–Nagumo equation illustrates its potency. Convergence analysis also shows that OPIM, unlike many other methods in literature, converges fast to exact analytical solutions of the nonlinear problems at lower order of approximations. © 2019
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Chromosomes , Genetic algorithms , Iterative methods , Partial differential equations , Perturbation techniques , Exact analytical solutions , Iteration method , Nagumo equation , Nonlinear partial differential equations , Population genetics , Semi-analytical techniques , Symbolic computation , Time-dependent coefficients , Nonlinear equations