Numerical Solution of Boundary Value Problems for Ordinary Differential Equations (Uri M. Ascher, Robert M. M. Mattheij, and Robert D. Russell)

SIAM Review ◽  
1989 ◽  
Vol 31 (4) ◽  
pp. 700-701
Author(s):  
Eugene Isaacson
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Boundary Value

Numerical Solution of the Beam Equation With Nonuniform Foundation Coefficient

1979 ◽  
Vol 46 (4) ◽  
pp. 901-904 ◽  
Author(s):  
M. Lentini
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
New Method ◽  
Beam Equation ◽  
Infinite Intervals

A new method for computing the solutions of the beam equation is given for the case of the problem of a pile. The method could be used for other problems where it is necessary to solve boundary-value problems for ordinary differential equations over semi-infinite intervals.

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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