scholarly journals A PROPOSAL FOR THE NUMERICAL SOLUTION OF THE BOUNDARY VALUE PROBLEM OF THE LINEAR HOMOGENEOUS DIFFERENTIAL EQUATION SYSTEM

1968 ◽  
Vol 24 (12) ◽  
pp. 579-582
Author(s):  
Eiichi Kuze ◽  
Tetsuya Sakai ◽  
Eiichiro Tazaki
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Numerical Solution ◽  
Boundary Value ◽  
Equation System ◽  
Differential Equation System ◽  
Homogeneous Differential Equation ◽  
Linear Homogeneous Differential Equation

A New Method and Applications of the Boundary Value Problem of Differential Equation

2014 ◽  
Vol 937 ◽  
pp. 695-699
Author(s):  
Hong E Li ◽  
Xiao Xu Dong ◽  
Shun Chu Li ◽  
Dong Dong Gui ◽  
Cong Yin Fan
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Kernel Function ◽  
Boundary Value ◽  
Outer Boundary ◽  
Seepage Flow ◽  
Petroleum Engineering ◽  
Constructive Method ◽  
Linear Homogeneous Differential Equation ◽  
The Mathematical Model

The similar structure of solution for the boundary value problem of second order linear homogeneous differential equation has been studied. Based on the analysis of the relationship between similar structure of solution, its kernel function, the equation and boundary conditions, similar constructive method (shortened as SCM) of solution is obtained. According to the SCM, the similar structure of solution and its kernel function are constructed for the mathematical model of homogeneous reservoir which considers the influence of bottom-hole storage and skin effect under the infinite outer boundary condition. The SCM is a new and innovative way to solve boundary value problem of differential equation and seepage flow theory, which is especially used in Petroleum Engineering.

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