Existence and uniqueness of monotone and bounded solutions for a finite-difference discretization à la Mickens of the generalized Burgers–Huxley equation

Interdiffusion in many dimensions: mathematical models, numerical simulations and experiment

“…To approximate the remaining derivatives, the central, forward and back difference quotients will be used. Moreover, the terms D i (N i ) in the first (s − 1) equations in equation (27) will be approximated by…”

“…We define an implicit difference scheme for the elliptic subsystem on the potential F in equations (25) to (27). It is a system of linear algebraic equations of the form Then we define an implicit difference scheme for the parabolic subsystem on the concentrations c i , i = 1, .…”

“…Numerical methods that preserve some futures of a continuous model are very important and interesting from a physical and mathematical point of view. For example, boundedness-, positivity-or monotonicity-preserving numerical methods were studied in [25][26][27][28][29][30][31][32][33][34][35] and in the references therein. We prove that the implicit difference schemes given have a unique solution and that the difference methods are consistent.…”

A Numerical Schemefor the Probability Density of the First Hitting Time for Some Random Processes

“…In that sense, the scheme proposed in this work will be a structure-preserving model [29,30]. Structure-preserving models have been designed to preserve the positivity and the symmetry of the solutions of Fisher-type equations [31], the monotonicity and boundedness of numerical model for Burgers-Huxley-type equations [32], the positivity of high-order Galerkin schemes for compressible Euler equations [33], the positivity and boundedness of numerical schemes for space-time fractional predator-prey models [34] and the energy and symmetry of Riesz space-fractional nonlinear wave equations [35]. In summary, the development of structure-preserving numerical techniques has been an important factor in problems where particular features of the solutions are physically meaningful [35,36].…”

Numerical solution of generalized Burger’s-Huxley equation using local radial basis functions

“…These include optimal homotopy asymptotic method by Ali et al (2012), Adomian decomposition technique by Ismail et al (2004), Haar wavelet method by Celik (2012), computational meshless method by Khattak (2009). Many other techniques can be found in references (Mittal and Tripathi, 2015;Jiwari el al., 2013;El-Kady et al, 2013;Macías-Díaz and Szafrańska, 2014;Ervin et al, 2015).…”