Construction Solutions of Ordinary and Partial Differential Equations using the Analytical and Numerical Methods
Author: Turkia Dhawi Alqurashi
Master of Mathematics (Numerical Analysis), College of Science, Shaqra University, Saudi Arabia
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.
Regular Differential Equations, Partial Equations, Regular Differential Equivalent Solutions.