Boundary value problems for certain classes of loaded differential equations and solving them by finite difference methods

2008 ◽  
Vol 48 (9) ◽  
pp. 1581-1590 ◽  
Author(s):  
A. A. Alikhanov ◽  
A. M. Berezgov ◽  
M. X. Shkhanukov-Lafishev
Keyword(s):  
Finite Difference ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Finite Difference Methods ◽  
Difference Methods

On finite-difference methods for the numerical solution of boundary-value problems

1961 ◽  
Vol 262 (1309) ◽  
pp. 219-236 ◽  
Keyword(s):  
Partial Differential Equations ◽  
Finite Difference ◽  
Differential Equations ◽  
Numerical Solution ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Finite Difference Methods ◽  
Elliptic Type ◽  
Partial Differential ◽  
Difference Methods

We consider the application of finite-difference methods to the numerical solution of boundary-value problems. In particular we are concerned to study the feasibility and con­vergence of the difference-correction method for the solution of partial differential equations of elliptic type. These topics form the subject matter for §§ 3 to 6. The material of the first two sections is intended to serve as a preliminary for the main discussion. The topics considered here are finite difference formulae for numerical differentiation, and finite difference methods for the solution of partial differential equations.

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