Asymptotic Bounds for the Time-Periodic Solutions to the Singularly Perturbed Ordinary Differential Equations

The periodical in time problem for singularly perturbed second order linear ordinary differential equation is considered. The boundary layer behavior of the solution and its first and second derivatives have been established. An example supporting the theoretical analysis is presented

Uniform numerical approximation for parameter dependent singularly perturbed problem with integral boundary condition

WOS: 000441460300026In this paper, a parameter-uniform numerical method for a parameterized singularly perturbed ordinary differential equation containing integral boundary condition is studied. Asymptotic estimates on the solution and its derivatives are derived. A numerical algorithm based on upwind finite difference operator and an appropriate piecewise uniform mesh is constructed. Parameter-uniform error estimate for the numerical solution is established. Numerical results are presented, which illustrate the theoretical results

A numerical method for a second order singularly perturbed Fredholm integro-differential equation

The boundary-value problem for a second order singularly perturbed Fredholm integro-differential equation was considered in this paper. For the numerical solution of this problem, we use an exponentially fitted difference scheme on a uniform mesh which is succeeded by the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with the weight and remainder terms in integral form. Also, the method is first order convergent in the discrete maximum norm. Numerical example shows that recommended method has a good approximation characteristic.WOS:0006611395000042-s2.0-8510854604

Error Estimates for Differential Difference Schemes to Pseudo-Parabolic Initial-Boundary Value Problem With Delay

We consider the one dimensional initial-boundary Sobolev problem with delay. For solving this problem numerically, we construct fourth order differential-difference scheme and obtain the error estimate for its solution. Further we use the appropriate Runge- Kutta method for the realization of our differential-difference problem

Three layer difference method for linear pseudo-parabolic equation with delay

This paper deals with the study a finite-difference approximation of the one dimensional initial-boundary value problem for a pseudo-parabolic equation containing time delay in second derivative. We propose three layer difference scheme and obtain the error estimates for its solution. Based on the method of energy estimates the fully discrete scheme is shown to be convergent of order four in space and order two in time. Numerical results are presented to illustrate the theoretical findings. (C) 2021 Elsevier B.V. All rights reserved.WOS:0006970298000062-s2.0-8511440298

A Numerical Method for a Singularly Perturbed Three-Point Boundary Value Problem

The purpose of this paper is to present a uniform finite difference method for numerical solution of nonlinear singularly perturbed convection-diffusion problem with nonlocal and third type boundary conditions. The numerical method is constructed on piecewise uniform Shishkin type mesh. The method is shown to be convergent, uniformly in the diffusion parameter ε, of first order in the discrete maximum norm. Some numerical experiments illustrate in practice the result of convergence proved theoretically

Stability inequalities for the delay pseudo-parabolic equations

This paper deals with the initial-boundary value problem for linear pseudo-parabolic equation. Using the method of energy estimates the stability bounds obtained for the considered problem. Illustrative example is also presented. © 2019 Academic Publications

A RESENT SURVEY ON NUMERICAL METHODS FOR SOLVING SINGULARLY PERTURBED PROBLEMS

6th International Conference on Control and Optimization with Industrial Applications (COIA) -- JUL 11-13, 2018 -- Baku, AZERBAIJANWOS: 000463893800023…Minist Transport Commun & High Technologies Republ Azerbaijan, Baku State Univ, Inst Appl Mat

A Fitted Second-Order Difference Method for a Parameterized Problem with Integral Boundary Condition Exhibiting Initial Layer

In this paper, the homogeneous type fitted difference scheme for solving singularly perturbed problem depending on a parameter with integral boundary condition is proposed. We prove that the method is O(N(-2)lnN) uniform convergent on Shishkin meshes. Numerical results are also presented.WOS:0006407763000012-s2.0-8510439956