scholarly journals Finite Difference Method for Solving a System of Third-Order Boundary Value Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Muhammad Aslam Noor ◽  
Eisa Al-Said ◽  
Khalida Inayat Noor
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Boundary Value Problems ◽  
Difference Method ◽  
Boundary Value ◽  
Approximate Solutions ◽  
Obstacle Problems ◽  
Third Order ◽  
Flow Problems ◽  
Coating Flow

We develop a new-two-stage finite difference method for computing approximate solutions of a system of third-order boundary value problems associated with odd-order obstacle problems. Such problems arise in physical oceanography (Dunbar (1993) and Noor (1994), draining and coating flow problems (E. O. Tuck (1990) and L. W. Schwartz (1990)), and can be studied in the framework of variational inequalities. We show that the present method is of order three and give numerical results that are better than the other available results. Numerical example is presented to illustrate the applicability and efficiency of the new method.

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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