Stability analysis for singularly perturbed differential equations by the upwind difference scheme

2013 ◽  
Vol 30 (5) ◽  
pp. 1595-1613
Author(s):  
Zi Cai Li ◽  
Yimin Wei ◽  
Hung Tsai Huang ◽  
John Y. Chiang
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Difference Scheme ◽  
Singularly Perturbed ◽  
Upwind Difference Scheme

A HYBRID DIFFERENCE SCHEME FOR SINGULARLY PERTURBED SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS WITH DISCONTINUOUS CONVECTION COEFFICIENT AND MIXED TYPE BOUNDARY CONDITIONS

2008 ◽  
Vol 05 (04) ◽  
pp. 575-593 ◽  
Author(s):  
R. MYTHILI PRIYADHARSHINI ◽  
N. RAMANUJAM
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Difference Scheme ◽  
Ordinary Differential Equations ◽  
Mixed Type ◽  
Second Order ◽  
Singularly Perturbed ◽  
Convection Coefficient ◽  
Type Boundary ◽  
Numerical Derivative

This paper presents, a hybrid difference scheme for singularly perturbed second order ordinary differential equations with a small parameter multiplying the highest derivative with a discontinuous convection coefficient subject to mixed type boundary conditions. Error bounds for the numerical solution and numerical derivative are established. Numerical results are provided to illustrate the theoretical results.

Exponentially fitted difference scheme for singularly perturbed mixed integro-differential equations

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Musa Cakir ◽  
Baransel Gunes
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Difference Scheme ◽  
Singularly Perturbed ◽  
Stability And Convergence ◽  
Uniform Mesh ◽  
Numerical Examples ◽  
Exponentially Fitted ◽  
The Stability ◽  
Exponentially Fitted Difference Scheme

Abstract In this study, singularly perturbed mixed integro-differential equations (SPMIDEs) are taken into account. First, the asymptotic behavior of the solution is investigated. Then, by using interpolating quadrature rules and an exponential basis function, the finite difference scheme is constructed on a uniform mesh. The stability and convergence of the proposed scheme are analyzed in the discrete maximum norm. Some numerical examples are solved, and numerical outcomes are obtained.

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