Numerical simulation of nonlinear Schro¨dinger systems: a new conservative scheme
Applied Mathematics and Computation
Positivity of Runge-Kutta and diagonally split Runge-Kutta methods
Applied Numerical Mathematics - Selected papers on eighth conference on the numerical treatment of differential equations 1-5 September 1997, Alexisbad, Germany
Discretizations of nonlinear differential equations using explicit nonstandard methods
Journal of Computational and Applied Mathematics
High order conservative difference methods for 2D drift-diffusion model on non-uniform grid
Proceedings of the fourth international conference on Spectral and high order methods (ICOSAHOM 1998)
A nonstandard finite-difference scheme for the Lotka--Volterra system
Applied Numerical Mathematics
Symmetry-preserving discretization of turbulent flow
Journal of Computational Physics
Variable-order finite elements and positivity preservation for hyperbolic PDEs
Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs
Applied Numerical Mathematics
Numerical methods for the generalized Fisher-Kolmogorov-Petrovskii-Piskunov equation
Applied Numerical Mathematics
Structure preserving stochastic integration schemes in interest rate derivative modeling
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
A high order accurate conservative remapping method on staggered meshes
Applied Numerical Mathematics
Strong stability preserving hybrid methods
Applied Numerical Mathematics
ENO adaptive method for solving one-dimensional conservation laws
Applied Numerical Mathematics
A boundedness-preserving finite-difference scheme for a damped nonlinear wave equation
Applied Numerical Mathematics
Mathematics and Computers in Simulation
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In this work, we propose a finite-difference scheme to approximate the solutions of a generalization of the classical, one-dimensional, Newell-Whitehead-Segel equation from fluid mechanics, which is an equation for which the existence of bounded solutions is a well-known fact. The numerical method preserves the skew-symmetry of the problem of interest, and it is a non-standard technique which consistently approximates the solutions of the equation under investigation, with a consistency of the first order in time and of the second order in space. We prove that, under relatively flexible conditions on the computational parameters of the method, our technique yields bounded numerical approximations for every set of bounded initial estimates. Some simulations are provided in order to verify the validity of our analytical results. In turn, the validity of the computational constraints under which the method guarantees the preservation of the boundedness of the approximations, is successfully tested by means of computational experiments in some particular instances.