an efficient numerical method for singularly perturbed second order ordinary differential equation
Authors
abstract
in this paper an exponentially fitted finite difference method is presented for solving singularly perturbed two-point boundary value problems with the boundary layer. a fitting factor is introduced and the model equation is discretized by a finite difference scheme on an uniform mesh. thomas algorithm is used to solve the tri-diagonal system. the stability of the algorithm is investigated. it is shown that the proposed technique is of first order accurate and the error constant is independent of the perturbation parameter. several problems are solved and numerical results are presented to support the theoretical error bounds established.
similar resources
An efficient numerical method for singularly perturbed second order ordinary differential equation
In this paper an exponentially fitted finite difference method is presented for solving singularly perturbed two-point boundary value problems with the boundary layer. A fitting factor is introduced and the model equation is discretized by a finite difference scheme on an uniform mesh. Thomas algorithm is used to solve the tri-diagonal system. The stability of the algorithm is investigated. It ...
full textNumerical method for singularly perturbed fourth order ordinary differential equations of convection-diffusion type
In this paper, we have proposed a numerical method for singularly perturbed fourth order ordinary differential equations of convection-diffusion type. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and finite difference method. In order to get a numerical solution for the derivative of the solution, the given interval is divided in...
full textnumerical method for singularly perturbed fourth order ordinary differential equations of convection-diffusion type
in this paper, we have proposed a numerical method for singularly perturbed fourth order ordinary differential equations of convection-diffusion type. the numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and finite difference method. in order to get a numerical solution for the derivative of the solution, the given interval is divided in...
full textNumerical method for a system of second order singularly perturbed turning point problems
In this paper, a parameter uniform numerical method based on Shishkin mesh is suggested to solve a system of second order singularly perturbed differential equations with a turning point exhibiting boundary layers. It is assumed that both equations have a turning point at the same point. An appropriate piecewise uniform mesh is considered and a classical finite difference scheme is applied on t...
full textAsymptotic Numerical Method for Singularly Perturbed Third Order Ordinary Differential Equations with a Discontinuous Source Term
A class of singularly perturbed two point Boundary Value Problems (BVPs) of reaction-diffusion type for third order Ordinary Differential Equations (ODEs) with a small positive parameter (ε) multiplying the highest derivative and a discontinuous source term is considered. The BVP is reduced to a weakly coupled system consisting of one first order ordinary differential equation with a suitable i...
full textOn the Numerical Solution for Singularly Perturbed Second-order ODEs
In this article we consider the approximation of singularly perturbed boundary value problems using a local adaptive grid h-refinement for finite element method, the variation iteration method and the homotopy perturbation method. The solution to such problems contains boundary layers which overlap and interact and the numerical approximation must take this into account in order for the resulti...
full textMy Resources
Save resource for easier access later
Journal title:
journal of mathematical modelingPublisher: university of guilan
ISSN 2345-394X
volume 3
issue 1 2015
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023