Search
Search Results
-
Nonstandard Finite Difference Scheme for the Epidemic Model with Vaccination
For the epidemic model with vaccination we present a new nonstandard finite difference scheme by using an exponential integrator to discretize...
-
Nonstandard finite difference schemes for linear and non-linear Fokker–Planck equations
The goal of this paper is to develop a nonstandard finite difference-based numerical technique for solving the one-dimensional linear and non-linear...
-
A generalized model for the population dynamics of a two stage species with recruitment and capture using a nonstandard finite difference scheme
The aim of this work is to formulate and analyze a new and generalized discrete-time population dynamics model for a two-stage species with...
-
On the Advantages of Nonstandard Finite Difference Discretizations for Differential Problems
AbstractThe goal of this work is to highlight the advantages of using NonStandard Finite Difference (NSFD) numerical schemes for the solution of...
-
A class of second-order and dynamically consistent nonstandard finite difference schemes for nonlinear Volterra’s population growth model
In a recent work (Hoang in Math Comput Simul 199:359–373, 2022), a class of nonstandard finite difference (NSFD) schemes preserving the positivity...
-
Extending Nonstandard Finite Difference Scheme for SIR Epidemic Model
When constructing a non-standard difference scheme for the differential equations, denominator of the discrete derivative is chosen as the functions...
-
Wavelet-based approximation with nonstandard finite difference scheme for singularly perturbed partial integrodifferential equations
A non-standard finite difference scheme with Haar wavelet basis functions is constructed for the convection–diffusion type singularly perturbed...
-
Dynamically consistent nonstandard finite difference schemes for a virus-patch dynamic model
The aim of this work is to formulate and analyze nonstandard finite difference (NSFD) schemes for a recognized virus-patch dynamic model. We...
-
Model Theory of Nonstandard Structures with Applications
Every infinite mathematical structure \( \mathcal{M} \) has...
-
A nonstandard finite difference scheme for the modeling and nonidentical synchronization of a novel fractional chaotic system
The aim of this paper is to introduce and analyze a novel fractional chaotic system including quadratic and cubic nonlinearities. We take into...
-
Higher-Order Finite-Difference Schemes for Nonlinear Two-Point Boundary Value Problems
We present a family of high-order multi-point finite difference methods for solving nonlinear two-point boundary value problems. The family involves...
-
Erratum to: On the Advantages of Nonstandard Finite Difference Discretizations for Differential Problems
An Erratum to this paper has been published: https://doi.org/10.1134/S1995423922040127
-
An Efficient Non-standard Finite Difference Scheme for Solving Distributed Order Time Fractional Reaction–Diffusion Equation
In this article, a nonstandard finite difference scheme is proposed for solving the distributed order time-fractional reaction–diffusion equation. In...
-
Compact finite difference schemes with high resolution characteristics and their applications to solve Burgers equation
In this article, non-standard compact finite difference schemes are constructed for the numerical approximation to first- and second-order...
-
The Allure of Infinitesimals: Sergio Albeverio and Nonstandard Analysis
I give a survey of Sergio Albeverio’s work in nonstandard analysis, covering applications to operator theory, stochastic analysis, Dirichlet forms,...
-
Multigrid with Nonstandard Coarse-Level Operators and Coarsening Factors
We consider the numerical solution of Poisson’s equation on structured grids using geometric multigrid with nonstandard coarse grids and coarse-level...
-
Realization of the Exact Three-Point Finite-Difference Schemes for the System of Second-Order Ordinary Differential Equations
We consider an exact three-point finite-difference scheme (EDS) for the Dirichlet boundary-value problem for a system of second-order ordinary...
-
Euler’s Series for Sine and Cosine: An Interpretation in Nonstandard Analysis
In chapter VIII of Introductio in analysin infinitorum, Euler derives a series for sine, cosine, and the formula...
-
Numerical dynamics of nonstandard finite difference schemes for a Logistics model with feedback control
In this paper, we construct nonstandard finite difference (NSFD) schemes that preserve essential qualitative properties of a Logistics model with...
