Finite Element Method  
Finite Element Method
is a powerful method to compute numerical solutions to both Ordinary
Different Equations(ODEs), and Partial Differential Equations (PDEs).
However it involves quite a few advanced concepts in mathematics, such
as the functional spaces, minimizing a functional etc. These concepts are
hard to grasp . These pages are designed to help you to understand
the Finite Element Method in an application to ODEs.
Advanced Mathematical Concepts: In this page we will discuss several advanced concepts that appear in the development of the Finite Element Method. The first of these concepts are functional or functions of functions. The second concept is minimizing functionals, and the third deals with the basis of a vector space and inner products. Finite
Different Method ODE Example 1: In this page we will apply the method to solve the boundary problem y'' + 2y = x, for 0< x < 1 and y(0) = y(1) = 0, with two base functions. We will give details of the computation and the Mathematica code as well. The graph of the approximated function is also given. Example
2: Here we will apply the method to solve the boundary problem
y'' + 2y = x, for 0< x < 1 and y(0) = y(1) = 0, with four
base functions. We will give details of the computation and the Mathematica
code as well. The graph of the approximated function is also given.
With more basis function the computation is more complex and the approximation
is more accurate.
