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Published in:
01-09-2014
On an exact numerical simulation of solitary-wave solutions of the Burgers–Huxley equation through Cardano’s method
Published in: BIT Numerical Mathematics | Issue 3/2014
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Abstract
In this work, we develop an exact finite-difference methodology to approximate the solution of a diffusive partial differential equation with Burgers advection and Huxley reaction law. The model under investigation possesses solitary-wave solutions which are positive, bounded, and both spatially and temporally monotone. On the other hand, our computational model is a nonlinear technique for which the new approximations are provided as the roots of an uncoupled system of cubic polynomials, in which the constant coefficients are functions of the model parameters and the numerical step-sizes. In this system, each cubic equation is solved using Cardano’s formulas. The method proposed in this work preserves the positivity, the boundedness and the monotonicity of approximations, as well as the constant solutions of the continuous model. The simulations provided in this work show a good agreement with respect to the analytical solutions employed.