About the central difference method for singularly perturbed boundary value problems

1995 ◽  
Vol 17 (3) ◽  
pp. 333-346 ◽  
Author(s):  
Alessandra Papini
Keyword(s):  
Boundary Value Problems ◽  
Difference Method ◽  
Boundary Value ◽  
Singularly Perturbed ◽  
Central Difference ◽  
Central Difference Method

scholarly journals Fourth-order stable central difference with Richardson extrapolation method for second-order self-adjoint singularly perturbed boundary value problems

2019 ◽  
Vol 27 (1) ◽  
Author(s):  
Muslima Kedir Siraj ◽  
Gemechis File Duressa ◽  
Tesfaye Aga Bullo
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Mesh Size ◽  
Perturbation Parameter ◽  
Richardson Extrapolation ◽  
Second Order ◽  
Singularly Perturbed ◽  
Algebraic Equations ◽  
Central Difference ◽  
Convergence Of The Scheme

AbstractThis study introduces a stable central difference method for solving second-order self-adjoint singularly perturbed boundary value problems. First, the solution domain is discretized. Then, the derivatives in the given boundary value problem are replaced by finite difference approximations and the numerical scheme that provides algebraic systems of equations is developed. The obtained system of algebraic equations is solved by Thomas algorithm. The consistency and stability that guarantee the convergence of the scheme are investigated. The established convergence of the scheme is further accelerated by applying the Richardson extrapolation which yields sixth order convergent. To validate the applicability of the method, two model examples are solved for different values of perturbation parameter ε and different mesh size h. The proposed method approximates the exact solution very well. Moreover, the present method is convergent and gives more accurate results than some existing numerical methods reported in the literature.

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