A Systematic Review on the Solution Methodology of Singularly Perturbed Differential Difference Equations
نویسندگان
چکیده
This review paper contains computational methods or solution methodologies for singularly perturbed differential difference equations with negative and/or positive shifts in a spatial variable. survey limits its coverage to singular perturbation arising the modeling of neuronal activity and developed by numerous researchers between 2012 2022. The covered ordinary delay small large shift(s), differential–differential mixed partial shift(s) differential–difference type. main aim this is find out what numerical asymptotic were last ten years solve such problems. Further, it aims stimulate develop new robust solving families problems under consideration.
منابع مشابه
A method based on the meshless approach for singularly perturbed differential-difference equations with Boundary layers
In this paper, an effective procedure based on coordinate stretching and radial basis functions (RBFs) collocation method is applied to solve singularly perturbed differential-difference equations with layer behavior. It is well known that if the boundary layer is very small, for good resolution of the numerical solution at least one of the collocation points must lie in the boundary layer. In ...
متن کاملA Parameter Uniform Numerical Scheme for Singularly Perturbed Differential-difference Equations with Mixed Shifts
In this paper, we consider a second-order singularly perturbed differential-difference equations with mixed delay and advance parameters. At first, we approximate the model problem by an upwind finite difference scheme on a Shishkin mesh. We know that the upwind scheme is stable and its solution is oscillation free, but it gives lower order of accuracy. So, to increase the convergence, we propo...
متن کاملThe numerical solution of the singularly perturbed differential-difference equations based on the Meshless method
In this paper, we describe a meshless approach to solve singularly perturbed differentialdifference equations of the second order with boundary layer at one end of the interval. In the numerical treatment for such type of problems, first we approximate the terms containing negative and positive shifts which converts it to a singularly perturbed differential equation. Next, a numerical scheme ba...
متن کاملNumerical Solution of Systems of Singularly Perturbed Differential Equations
Abstract — A survey is given of current research into the numerical solution of timeindependent systems of second-order differential equations whose diffusion coefficients are small parameters. Such problems are in general singularly perturbed. The equations in these systems may be coupled through their reaction and/or convection terms. Only numerical methods whose accuracy is guaranteed for al...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics
سال: 2023
ISSN: ['2227-7390']
DOI: https://doi.org/10.3390/math11051108