numerical method for singularly perturbed fourth order ordinary differential equations of convection-diffusion type

نویسندگان

joseph stalin christy roja

st. joseph's college, tamilnadu, india ayyadurai tamilselvan

bharathidasan university, tamilnadu, india

چکیده

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  into two subintervals called inner region (boundary layer region) and outer region. the shooting method  is applied to inner region whereas for the outer region, standard finite difference method is applied.  necessary error estimates are derived. computational efficiency and accuracy are verified through numerical examples.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Numerical 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...

متن کامل

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 ...

متن کامل

Asymptotic 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...

متن کامل

Multiscale Numerical Methods for Singularly Perturbed Convection-diffusion Equations

We present an efficient and robust approach in the finite element framework for numerical solutions that exhibit multiscale behavior, with applications to singularly perturbed convection-diffusion problems. The first type of equation we study is the convectiondominated convection-diffusion equation, with periodic or random coefficients; the second type of equation is an elliptic equation with s...

متن کامل

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 ...

متن کامل

An Asymptotic Numerical Method for Singularly Perturbed Weakly Coupled System of Convection-diffusion Type Differential Difference Equations

In this paper an asymptotic numerical method is suggested to solve singularly perturbed weakly coupled system of convectiondiffusion type second order ordinary differential equations with delay (negative shift) terms. An error estimate is derived in the supremum norm and it is found to be of order O(N−1 lnN) provided that ε ≤ CN−1, where ε is small perturbation parameter and N is the discretiza...

متن کامل

منابع من

با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید


عنوان ژورنال:
journal of mathematical modeling

جلد ۴، شماره ۱، صفحات ۷۹-۱۰۲

میزبانی شده توسط پلتفرم ابری doprax.com

copyright © 2015-2023