The method of finite differences in the theory of partial differential equations

1962 ◽  
pp. 77-104 ◽  
Author(s):  
O. A. Ladyženskaya
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Finite Differences ◽  
Partial Differential

scholarly journals Construction Solutions of Ordinary and Partial Differential Equations using the Analytical and Numerical Methods

2022 ◽  
Vol 3 (33) ◽  
pp. 103-120
Author(s):  
Turkia Dhawi Alqurashi ◽  
Keyword(s):  
Partial Differential Equations ◽  
Numerical Methods ◽  
Analytical Solution ◽  
Differential Equations ◽  
Finite Differences ◽  
Partial Differential ◽  
Internal Solution ◽  
Independent Variables ◽  
New Formula

In this paper we studied the solution of partial differential equations using numerical methods. The paper includes study of the solving partial differential equations of the type of parabolic, elliptic and hyperbolic, and the method of the net was used for the numerical nods, which represents a case of finite differences. We have two types of solution which are the internal solution and boundary solution. The internal solution is based on the internal nodes of the net. The boundary solution depends on the boundary nodes of the net, in addition to finding the analytical solution of the equations to compare the results. We also discussed solving the problem of Laplace, Poisson, for the importance of these equations in the applied side; Mat lab was used to find the values of tables for the values of border differences. We have derived a new formula for the solution of partial differential equations containing three independent variables.

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