scholarly journals High-order exponentially fitted difference schemes for singularly perturbed two-point boundary value problems

2018 ◽  
Vol 48 ◽  
pp. 329-347
Author(s):  
Miljenko Marušić
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
High Order ◽  
Difference Schemes ◽  
Singularly Perturbed ◽  
Point Boundary ◽  
Exponentially Fitted

scholarly journals A New Exponentially Fitted Numerical Integration Scheme for Solving Singularly Perturbed Two Point Boundary Value Problems

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Boundary Value Problems ◽  
Numerical Integration ◽  
Boundary Value ◽  
Singularly Perturbed ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Integration Scheme ◽  
Uniform Mesh ◽  
Point Boundary ◽  
Exponentially Fitted

: This article is concerned with an exponentially fitted numerical integration method based on uniform mesh for solving singularly perturbed two point boundary value problems. Exact and approximate rule of integration with finite difference approximation of first derivatives are used to derive a three term scheme. Theory of singular perturbation is used to introduce a fitting factor in the derived scheme. Thomas algorithm is employed to solve the resulting tridiagonal system of equations. Convergence of the proposed method is also analyzed. Solutions of several linear and nonlinear example problems are presented in terms of maximum absolute errors (MAE) to show the applicability of the proposed scheme. It is easily observed that the proposed method is able to approximate the solution very well.

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