A Numerical Solution of the Semi Linear Singularly Perturbed Boundary Value Problem Using Multi Region Finite Difference Method

2009 ◽  
Author(s):  
David Edwards Jr.
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Boundary Value Problem ◽  
Numerical Solution ◽  
Difference Method ◽  
Boundary Value ◽  
Singularly Perturbed

scholarly journals Finite-difference method for parameterized singularly perturbed problem

2004 ◽  
Vol 2004 (3) ◽  
pp. 191-199 ◽  
Author(s):  
G. M. Amiraliyev ◽  
Mustafa Kudu ◽  
Hakki Duru
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Theoretical Analysis ◽  
Boundary Value Problem ◽  
Numerical Solution ◽  
Difference Method ◽  
Singularly Perturbed ◽  
Singularly Perturbed Problem ◽  
First Order ◽  
Uniform Error Estimates

We study uniform finite-difference method for solving first-order singularly perturbed boundary value problem (BVP) depending on a parameter. Uniform error estimates in the discrete maximum norm are obtained for the numerical solution. Numerical results support the theoretical analysis.

scholarly journals the numerical solution of two point boundary value problem for the Helmholtz type equation by finite difference method with non regular step length between nodes

2021 ◽  
Vol 1 (1) ◽  
pp. 18-23
Author(s):  
Pramod Pandey
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Numerical Solution ◽  
Difference Method ◽  
Boundary Value ◽  
Type Equation ◽  
Step Length ◽  
Computational Results ◽  
Order Of Accuracy ◽  
Variable Step

In this article, we have presented a variable step finite difference method for solving second order boundary value problems in ordinary differential equations. We have discussed the convergence and established that proposed has at least cubic order of accuracy. The proposed method tested on several model problems for the numerical solution. The numerical results obtained for these model problems with known / constructed exact solution confirm the theoretical conclusions of the proposed method. The computational results obtained for these model problems suggest that method is efficient and accurate.

A new finite difference method for computing approximate solutions of boundary value problems including transition conditions

2021 ◽  
Vol 102 (2) ◽  
pp. 54-61
Author(s):  
S. Çavuşoğlu ◽  
◽  
O.Sh. Mukhtarov ◽  
◽  
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Differential Equations ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Difference Method ◽  
Numerical Solutions ◽  
Boundary Value ◽  
Approximate Solutions

This article is aimed at computing numerical solutions of new type of boundary value problems (BVPs) for two-linked ordinary differential equations. The problem studied here differs from the classical BVPs such that it contains additional conditions at the point of interaction, so-called transition conditions. Naturally, such type of problems is much more complicated to solve than classical problems. It is not clear how to apply the classical numerical methods to such type of boundary value transition problems (BVTPs). Based on the finite difference method (FDM) we have developed a new numerical algorithm for computing numerical solution of BVTPs for two-linked ordinary differential equations. To demonstrate the reliability and efficiency of the presented algorithm we obtained numerical solution of one BVTP and the results are compared with the corresponding exact solution. The maximum absolute errors (MAEs) are presented in a table.

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