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

2010 ◽  
Vol 2010 ◽  
pp. 1-17 ◽  
Author(s):  
Musa Çakır ◽  
Gabil M. Amiraliyev
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Numerical Method ◽  
Numerical Experiments ◽  
Diffusion Problem ◽  
Singularly Perturbed ◽  
Point Boundary ◽  
Convection Diffusion ◽  
First Order ◽  
Type Boundary

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 parameterε, of first order in the discrete maximum norm. Some numerical experiments illustrate in practice the result of convergence proved theoretically.

A finite-difference method for the numerical solution of the Sal’nikov thermokinetic oscillator problem

1995 ◽  
Vol 449 (1936) ◽  
pp. 255-271
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Stationary Point ◽  
Difference Method ◽  
Numerical Experiments ◽  
Euler Method ◽  
Initial Value ◽  
First Order ◽  
Highly Nonlinear ◽  
Implicit Finite Difference

A finite-difference method is developed for solving two coupled, ordinary differential equations that model a sequence of chemical reactions. The initial-value problem is highly nonlinear and involves three parameters. Various types of theoretical solution of this problem (the Sal’nikov thermokinetic oscillator problem) may be found, depending on these parameters; this is because the stationary point is surrounded by up to two limit cycles. The well-known, first-order, explicit Euler method and an implicit finite difference method of the same order are used to compute the solution. It is shown that this implicit method may, in fact, be used explicitly and extensive numerical experiments are made to confirm the superior stability properties of the alternative method.

Robust Finite Difference Method for Singularly Perturbed Two-Parameter Parabolic Convection-Diffusion Problems

2020 ◽  
pp. 2050034
Author(s):  
Tesfaye Aga Bullo ◽  
Gemechis File Duressa ◽  
Guy Aymard Degla
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Perturbation Parameter ◽  
Accurate Solution ◽  
Singularly Perturbed ◽  
Parabolic Problems ◽  
Uniform Mesh ◽  
Convection Diffusion ◽  
Diffusion Problems

Robust finite difference method is introduced in order to solve singularly perturbed two parametric parabolic convection-diffusion problems. In order to discretize the solution domain, Micken’s type discretization on a uniform mesh is applied and then followed by the fitted operator approach. The convergence of the method is established and observed to be first-order convergent, but it is accelerated by Richardson extrapolation. To validate the applicability of the proposed method, some numerical examples are considered and observed that the numerical results confirm the agreement of the method with the theoretical results effectively. Furthermore, the method is convergent regardless of perturbation parameter and produces more accurate solution than the standard methods for solving singularly perturbed parabolic problems.

scholarly journals The Sdfem for a Convection-diffusion Problem with Two Small Parameters

2003 ◽  
Vol 3 (3) ◽  
pp. 443-458 ◽  
Author(s):  
Hans-Görg Roos ◽  
Zorica Uzelac
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Experiments ◽  
Diffusion Problem ◽  
Shishkin Mesh ◽  
Singularly Perturbed ◽  
Convection Diffusion ◽  
Small Parameters ◽  
Perturbation Parameters ◽  
Theoretical Results

AbstractA singularly perturbed convection-diffusion problem with two small parameters is considered. The problem is solved using the streamline-diffusion finite element method on a Shishkin mesh. We prove that the method is convergent independently of the perturbation parameters. Numerical experiments support these theoretical results.

scholarly journals A Hybrid Differential Transforms and Finite Difference Method to Numerical Solution of Convection–Diffusion Equation

2021 ◽  
Vol 8 (6) ◽  
pp. 90-94
Author(s):  
Noorulhaq Ahmadi ◽  
Mohammadi Khan Mohammadi
Keyword(s):  
Partial Differential Equations ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Diffusion Equation ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Difference Method ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Type Boundary

In this work, we discuss a hybrid-based method on differential transforms and a finite difference method to numerical solution of convection–diffusion equation with Dirichlet’s type boundary conditions. The developed method is tested on various problems and the numerical results are reported in tabular and figure form. This method can be easily extended to handle non-linear convection–diffusion partial differential equations.

Sign in / Sign up

Export Citation Format

Share Document